Playing card for magicians

Abstract

Playing card (1), comprising four sides (3, 4, 5, 6) defining an outline (2), wherein the four sides (3, 4, 5, 6) comprise two major sides (3, 4) parallel to each other and two minor sides (5, 6) parallel to each other, wherein the outline (2) defined by the four sides (3, 4, 5, 6) is a chiral geometric figure such as not to be superimposable on its own mirror image.

Description

[0001] Playing card for magicians

[0002] TECHNICAL FIELD

[0003] The present invention relates to a playing card for magicians . Furthermore , the present invention relates to a deck of cards comprising a plurality of said playing cards .

[0004] BACKGROUND

[0005] Among the branches of artful sleight of hand tricks there is what is called card magic, in which the magician creates illusionistic ef fects by using playing cards . The artful sleight of hand tricks with playing cards can take place using one or more decks of cards , only a few cards or even a single playing card .

[0006] The one mostly used for card magic games is the poker deck which consists of 52 cards with French suits , measuring 63 . 5mm x 88 . 8mm . Other types of decks are used for these games . For example , bridge decks are employed that comprise smaller cards ( 56mm x 88 . 9mm) than poker cards . However, poker cards are the most frequently used since their si ze of fers a larger surface on which to exert pressure and therefore easier execution of some illusionism techniques .

[0007] In addition to a speci fic skill in the technique and card handling, the magician can use special cards and decks to perform some illusionist games .

[0008] For example , use can be made of blank cards that are either blank with printed back or blank on both sides . In addition, double-back or double- faced cards can be used which are cards that have a back or face printed on both sides. The two backs can be the same colour and pattern or different colour or pattern. The same applies to the faces which may be the same or different.

[0009] To help the magician recognize specific cards, use can also be made of decks of cards that have a particular structure recognizable to the touch. For example, there is what is called the Svengali deck which is made up of half of all the same cards, and half of all different cards. The peculiarity of this deck lies in the fact that the same cards are about 1mm shorter, and therefore if positioned alternately with respect to the different cards, it allows shuffling the deck, showing the spectator only the different cards.

[0010] Another particular type of deck is what is called the conical deck. In this deck, the cards have a slightly trapezoidal shape, so that a card rotated by 180 degrees is distinguishable to the touch from the others, but looks perfectly identical to the others .

[0011] Patents or patent applications relating to decks of cards for magicians having cards with particular outlines are known in the literature.

[0012] US 347,192 is an 1886 document describing a particular playing card. The outline of the card has a parallelogram shape. Its objective is to ensure a firmer and more ergonomic grip of the deck, facilitating the dealer in dealing the cards and recomposing the deck in order to deal it again. In addition, this document highlights the fact that no card can be inadvertently flipped, as the corners would clearly be out of outline by 4 cm, which is not avoidable in standard decks. However, this approach lacks any reference to finding a previously selected specific card within the deck.

[0013] US 2, 683, 604 is also a rather old document (1954) describing a playing card with a parallelogram shape. Reduced indexes on both the upper right and lower left are added in order to facilitate reading in the case of a greater plurality of cards in hand, as in the game of rummy. Although this document describes the presence of an oblique cut of about two centimetres on the shorter sides, raising the right corner on the horizontal plane, to facilitate the reading of the micro indexes, there is no reference to the possibility of easily extracting a card from a deck of cards that are apparently all identical .

[0014] CN 93221230 describes a playing card used exclusively in the traditional Chinese game "Mo Shu", similar to the Italian game " Zecchinetta" . Its composition alternates "various cards" with "changing cards", allowing the dealer to peek at the next card with a quick movement on the corners and then decide whether or not to change it.

[0015] This document defines these cards as "magical" because playing with these cards improves people's thinking and their ability to observe, judge and solve logic in problems, increasing entertainment activities in people's daily lives. However, the application of this card is limited to a specific context of the "Mo Shu" game and does not have the intent to select one or more cards and then bring them to light from the deck itself. The purpose shown in this document is to print half a deck on one face and the other half on the opposite face, to replace the "various cards" with "changed cards" if necessary. Although useful in their purpose of playing il lusion, standard and special decks ( such as conical decks ) currently available are limited in terms of the magician ' s ability to distinguish one card from another simply to the touch, in a well-shuf fled deck .

[0016] Therefore , it is an obj ect of the present invention to provide a playing card and thus a deck of playing cards composed exclusively of such cards perfectly identical to each other which have properties such as to allow the magician to identi fy one or more cards from the rest of the deck in a simple and fast way and to extract said card from the deck in a simple and fast way .

[0017] DESCRIPTION OF THE INVENTION

[0018] These obj ects are achieved by a playing card and a deck of cards according to the claims at the end of the present description .

[0019] In a first aspect of the invention there is provided a playing card comprising four sides defining an outline , wherein the four sides comprise two maj or sides parallel to each other and two minor sides parallel to each other . The playing card is characteri zed in that the outline defined by the four sides is a chiral geometric figure such as not to be superimposable on its mirror image .

[0020] Unlike traditional cards , the playing card described here has a spatial arrangement of the points that form a chiral outline , making it impossible to superimpose it perfectly on its own mirror image . These playing cards are enantiomeric with each other in all their perimeter points , despite having the same geometric properties . The perimeter delimitation of these playing cards avoids the need for rotating power, since even i f the poles are reversed, their outline remains unchanged . This allows these cards to show the same behaviour as traditional or conical decks , which are not chiral , or the desired chiral behaviour as needed .

[0021] The interaction between two playing cards according to the present disclosure can be di f ferent , j ust like a right hand shaking another hand and can distinguish whether the hand is left or right through stereospeci fic reactions .

[0022] The standard decks of cards , on the other hand, have superimposable images in three dimensions , and the conical decks , although achiral , have superimposable mirror images with di f ferences in points highlighted through a 180-degree rotation on a plane . In addition, standard or conical decks have infinite planes of symmetry in their length or width, being identical and superimposable on their reflected image , being devoid of the property of chirality . In addition, in these decks , any two cards are not enantiomers in their speci fic interaction when pole reversal occurs .

[0023] In addition, known decks of cards , such as those described in the patents mentioned above , do not refer to playing cards that are devoid of identity, that is , that are not apparently identi fiable from each other by a spectator . The cards of the deck described here can for example all be identical to each other ( for example blank, without any imprinted figure ) and can be used to allow a spectator to select a card ( or several cards ) and mark one of the faces of the card with words , signatures , initials or symbols thus making it unique . In this way, it is possible to play a game in which said card, once reinserted into the deck without the marked face being visible , can be easily found inside the deck itsel f in a simple and fast way .

[0024] In a second aspect of the invention there is provided a deck of cards comprising a plurality of playing cards according to the first aspect .

[0025] The deck of cards described here of fers numerous applications in the magic industry thanks to the property of the chirality of the individual playing cards . Through a kinetic resolution, it is in fact possible to identi fy and separate one or more speci fic cards from the rest of the deck, either by perceiving the asymmetry to the touch, or visually or through a mechanical separation thanks to the particular geometric configuration . Note that this is also possible with a well-shuf fled deck of cards . This would be impossible or extremely complicated with standard or special decks such as conical ones . In fact , "well- shuf fled deck" means a random rotation of the poles of the cards on the same plane , which would make even special decks unable to di f ferentiate one or more cards to the touch . In fact , conical decks would have the ability to di f ferentiate to the touch one or more cards only i f they were marginally shuf fled or i f there was a control of the poles by the dealer .

[0026] These and other aspects of the present invention will become more apparent in light of the following description of certain preferred embodiments described below . Fig . 1 shows the front and back of two cards according to the state of the art.

[0027] Fig. 2 shows the front and rear faces of a playing card according to an example.

[0028] Fig. 3 shows the front and rear faces of a playing card according to another example.

[0029] Fig. 4 shows in detail the upper edge of a playing card according to the examples of figures 2 and 3.

[0030] Fig. 5 shows the front face of a playing card according to a further example.

[0031] Fig. 6 shows the front and rear faces of a playing card according to an additional example.

[0032] Fig. 7 shows the front and rear faces of a playing card according to another example.

[0033] Figure 1 shows a schematic representation of two standard playing cards 9. In both cases, the playing card 9 is shown frontally (on the left) and rearwardly (on the right) . The face of the card represents a two of hearts. At the top, the playing card 9 has a rectangular outline, while at the bottom the outline is always rectangular but with chamfered corners. These are two classic outlines of standard playing cards 9, for example for poker or bridge. It is noted that in both cases the outline is an achiral and symmetrical geometric figure. In other words, imagining one of these cards reflecting in the mirror, the reflected image would be perfectly superimposable on the outline of the card itself.

[0034] Figures 2 and 3 instead represent two playing cards 1 modified with regard to the outline. It is noted that the sizes and proportions of the playing cards 1 illustrated in figures 2 and 3 are not real but purely indicative and serve to highlight the differences from the standard cards 9 of figure 1 that would otherwise be difficult to perceive with the naked eye. For example, both the playing card 1 of figure 2 and that of figure 3 would be perceived with the naked eye (or in any case by a spectator placed at a certain distance from the magician) as a playing card 9 with a rectangular outline (e.g. figure 1 above) .

[0035] Fig. 2 shows in particular the front face 7 (face) and the rear face 8 (back) of a playing card 1 according to the present disclosure. The card 1 comprises four sides 3, 4, 5, 6 defining the outline 2. The outline 2 is a parallelogram, wherein the two major sides 3, 4 and the two minor sides 5, 6 are parallel to each other.

[0036] The rear face 8 shown on the right in figure 2, can be imagined as the outline 2 of the mirror image of the front face 7 shown on the left in the same figure. It should be noted that the two outlines are not perfectly superimposable. In other words, the outline 2 is a chiral geometric figure.

[0037] According to one example, the minor side 5, 6 extends from a first major side 3 to a second major side 4 along a direction not orthogonal to the two major sides 3, 4 and defines a maximum deviation AL from the orthogonal direction at the second major side 4. As shown in figure 2, the playing card 1 shows a kind of inclined cut at the minor side 5 from the left to the right corner for a maximum value of deviation from the orthogonal direction of AL. Similarly, the card 1 comprises a second cut inclined and parallel to the first, on the other minor side 6 from left to right always with a maximum deviation of AL .

[0038] In one example, the maximum deviation AL is less than or equal to 1 mm, in particular less than or equal to 0.7 mm, more in particular less than or equal to 0.6 mm, even more in particular less than or equal to 0.5 mm.

[0039] Depending on the need, the playing card 1 may have different sizes. According to one embodiment, the major side 3, 4 may be comprised between 87.5 mm and 88.5 mm, in particular 88 mm. The minor side 5, 6 can be comprised between 62.5 mm and 63.5 mm, in particular 63 mm. The maximum deviation AL in this case can be 0.7 mm.

[0040] According to an alternative embodiment, the major side 3, 4 may be comprised between 88.5 mm and 89.5 mm, in particular 89 mm. The minor side 5, 6 can be comprised between 56.5 mm and 57.5 mm, in particular 57 mm. The maximum deviation AL in this case can be 0.6 mm.

[0041] According to a further alternative embodiment, the major side 3, 4 may be comprised between 83.5 mm and 84.5 mm, in particular 84 mm. The minor side 5, 6 can be comprised between 54.5 mm and 55.5 mm, in particular 55 mm. The maximum deviation AL in this case can be 0.5 mm. As mentioned above, the outline 2 is a parallelogram. As shown in figure 2, the minor sides 5, 6 are parallel to each other and have the same length. Similarly, the major sides 3, 4 are parallel to each other and have the same length. However, the length of the minor side 5, 6 is different from that of the major side 3, 4. Thus, according to one example, the outline 2 is a rhomboid parallelogram.

[0042] It is noted that the playing card 1 according to the present disclosure may take different shapes and sizes. Specifically, the chirality of the playing card 1 can possibly be obtained in alternative ways, for example with deviations with respect also to the major sides 3, 4 or with one or more protuberances or concavities along the major sides 3, 4 and / or minor sides 5, 6. However, the configurations described here, for example in the figures, represent one of the best configurations capable of creating the illusion to the spectator that the playing card 1 is identical to a standard playing card 9.

[0043] Figure 3 shows a playing card 1 similar to the playing card illustrated in figure 2. The playing cards 1 of the two figures 2 and 3 are identical except for a difference, i.e. the direction / corner of the cut of the minor side 5 from one major side 3 to the other major side 4. In other words, while in figure 2 the minor side 5 extends downwards with a maximum deviation of AL, in figure 3 the minor side 5 extends upwards, again with a maximum deviation of AL. The playing card 1 of figure 2 may advantageously be suitable for use with the right hand while the playing card 1 of figure 3 may advantageously be suitable for use with the left hand. As mentioned above, the major side 3, 4 forms an anglep with the minor side 5, 6 of the playing card 1. In particular, the angle p formed by these two sides is other than ninety degrees. This is shown in detail in figure 4. The playing card 1 illustrated on the left corresponds to a detail of the card 1 of figure 2. In this case, the minor side 5 extends with a downward deviation and forms with the major side 3 an angle p of less than ninety degrees. The angle a, i.e. the angle complementary to the angle p, is defined by the maximum deviation AL and the distance between the two major sides 3, 4. Advantageously, the angle a is less than 1.0 degree and may be comprised between 0.7 degrees and 0.5 degrees, in particular comprised between 0.64 degrees and 0.52 degrees. According to one example, the angle p formed between the minor side 3, 4 and the major side 5, 6 is comprised between 89.3 degrees and 89.5 degrees, in particular between 89.36 degrees and 89.48 degrees .

[0044] The playing card 1 illustrated on the right corresponds to a detail of the card 1 of figure 3. In this case, the minor side 5 extends with an upward deviation and forms with the major side 3 an angle p greater than ninety degrees. The angle a is defined by the maximum deviation AL and the distance between the two major sides 3, 4. Advantageously, the angle a is less than 1.0 degree and may be comprised between 0.7 degrees and 0.5 degrees, in particular comprised between 0.64 degrees and 0.52 degrees. According to one example, the angle p formed between the minor side 3, 4 and the major side 5, 6 is comprised between 90.5 degrees and 90.7 degrees, in particular between

[0045] 90.52 degrees and 90.64 degrees. Figure 5 shows a playing card 1 in which the outline 2 is a parallelogram with chamfered corners. It is noted that all the characteristics described above for the playing cards 1 of figures 2, 3 and 4, namely the chirality, the maximum deviation AL and the angles a and p, apply identically also to this type of card 1 whose only difference lies in the chamfered corners of the outline 2. Also in this case, the minor side 5, 6 extends from a first major side 3 to a second major side 4 along a direction not orthogonal to the two major sides 3, 4 and defines a maximum deviation AL from the orthogonal direction at the second major side 4. In particular, the card 1 illustrated on the left in figure 5 corresponds to the card shown in figure 2 while the card illustrated on the right in figure 5 corresponds to the card shown in figure 3.

[0046] Figure 6 shows a playing card 1 further comprising at least one recess 10 along one side 3, 4, 5, 6 of the outline 2. It is noted that all the characteristics described above for the playing cards 1 of figures 2, 3, 4 and 5, namely the chirality, the maximum deviation AL and the angles a and p, the chamfered corners, apply identically also to this type of card 1 whose only difference lies in the presence of at least one recess 10 in one of the sides of the outline 2. Specifically, figure 6 shows the same card 1 seen from one face (e.g. front 7) and seen from the opposite face (e.g. back 8) . The recess 10 represents an indentation in the card 1 or a region where part of the card 1 is missing. Therefore, the side of the card 1 having the recess 10 will have a generally straight profile except for this concave region where the profile will be indented according to a geometry defined by the recess 10. For example, the recess 10 may be a rounded cut in the shape of a semi-circle or semi-ellipse. According to one example, as shown in figure 6, the two major sides 3, 4 each comprise a recess 10. In this way, the card 1 comprises two recesses 10. In particular, the two recesses 10 are located near the corners of the card 1 in two regions opposite to each other. For example, a first recess 10 can be placed at the top right, i.e. near the top right corner of the card 1 while a second recess 10 can be placed at the bottom left, i.e. near the bottom left corner of the card 1.

[0047] According to one example, the recess 10 extends internally to the card 1 with a maximum depth d3, wherein d3 is comprised between 0.65 mm and 0.75 mm, in particular 0.7 mm.

[0048] Furthermore, the recess 10 may have a maximum extension dl along each of the two major sides 3, 4, wherein dl is comprised between 19 mm and 21 mm, in particular 20 mm.

[0049] In addition, the recess 10 may be at a distance d2 from a corner of the card 1, where d2 is comprised between 19 mm and 21 mm, in particular 20 mm. Specifically, the distance d2 represents the distance between the beginning of the recess 10 and the edge of the card. For example, considering the card to the left of figure 6, d2 represents the distance between the recess 10 (i.e. the outermost point of the recess 10 near the edge of the upper minor side 5) and the edge of the upper minor side 5 and the distance between the recess 10 (i.e. the outermost point of the recess 10 near the edge of the lower minor side 6) and the edge of the lower minor side 3.

[0050] Advantageously, dl is equal to d2. As mentioned above, the presence of one or more recesses 10 along the sides of the card 1 may be combined with the presence of the oblique cut along other sides of the card. In this way, the property of chirality is further emphasized.

[0051] In one example, the minor sides 5, 6 (upper and lower) of the card 1 have an oblique cut, made so as to be parallel and uniform. The cut on the upper side 5 has an inclination of 0.7 mm from the left vertex to the right vertex. Similarly, the bottom side 6 starts from the right corner and extends to the left with an equivalent depth (AL) of 0.7 mm, creating a distinctive profile on the minor sides of the card 1 (figures 2-5) . The major sides 3, 4 of the card 1 instead show a concave curvature (or recess) 10. Starting at about 20 mm from the upper left corner (d2) , a region of the card 1 is removed creating a curved cut with a depth of about 0.7 mm at the centre of the removed area (d3) and extension along the edge of the side of about 20 mm (dl) . This curvature continues as far as the lower left corner. A similar configuration is found on the right side, where the removal of the curved area starts from the lower right corner until it ends at the upper right corner (figure 6) . Figure 7 shows an example of card that integrates these two aspects. Of course, both the deviation AL and the recess size are not to scale with the actual dimensions from card 1 but have been emphasized in the figure to better clarify the concept.

[0052] The combination of the oblique cut and of the recess 10 on the card 1 produces a double chirality of the outline 2. This feature allows easy recognition and integration into magic performances, as it allows the selection and finding of one or more cards in a distinctive and intuitive way during sleight of hand games.

[0053] The playing card 1 described herein comprises a front face 7 and a rear face 8. Depending on the technique used and the type of illusion to be obtained, the front face 7 and the rear face 8 can take on different aspects.

[0054] In one example, both the front face 7 and the rear face 8 are unprinted blank faces. In other words, the playing card 1 is a card without elements printed on both faces, as shown in figure 7. This can be extremely advantageous for some types of card games if combined with the particular design of the just described card 1 that exploits the properties of chirality. In fact, in this way it is guaranteed that when selecting one or more cards, all the cards appear identical in the position of the face up (e.g. front face 7) . Once the spectator signs or jots down a secret word on the card 1, it acquires a unique identity. To preserve this new identity, the spectator flips the card face down (e.g. in the position with rear face 8 up) and shuffles the deck. The chirality of the outline 2 allows the development of fascinating techniques for finding the card 1 and cutting the deck with one hand.

[0055] It is noted that this example has been described for a deck of all-blank cards wherein each card 1 comprises a double aspect of chirality i.e. the presence of an oblique cut along the minor sides 5, 6 and of a recess 10 along the major sides 3, 4. However, the (blank) deck of cards may be similarly suitable for the same game even if each card comprises only one aspect of chirality, i.e. only the presence of an oblique cut along the minor sides 5 , 6 or only the presence of a recess 10 along the maj or sides 3 , 4 .

[0056] In another example , both the front face 7 and the rear face 8 are printed faces ( e . g . with the corresponding suits or with a pattern for the back) .

[0057] In a further example , one of the front face 7 or the rear face 8 is an unprinted blank face and the other is a printed face ( e . g . with corresponding suits or with a pattern for the back) .

[0058] The structure of the chiral outline present in the deck of cards described here can be assimilated to the conformation of molecules in chemistry, where the spatial arrangement of atoms determines the properties and behaviour of substances . Similarly, the distinctive design of the deck cards reflects a similar organi zation and symmetry, making them unique in their use and interaction .

[0059] Molecules can exist in chiral forms , i . e . structures that cannot be superimposed on their mirror image , giving them speci fic chemical and physical properties . Similarly, the chiral outline of the deck cards described here gives each card an identity feature that allows it to stand out in a magical and playful context .

[0060] Therefore , this deck of cards can be defined as a "molecular deck" , as its design is inspired by the principles of chirality and molecular symmetry . This analogy not only underlines the originality of the deck, but also the complexity and skill with which each card 1 interacts in the game , similar to the dynamics of interaction between molecules in nature . In conclusion, the key to the ef fectiveness of the deck of cards described here lies in its chiral structure , which of fers not only practical functionality for magicians , but also reflects the magni ficent order found in the world of molecules , making each performance a fascinating game of science and magic .

[0061] In order to satis fy further and contingent needs , a person skilled in the art may make numerous further modi fications and variations to the above described playing card 1 and card deck, all of which are included in the scope of protection of the present invention, as defined by the attached claims .

Claims

CLAIMS1. Playing card (1) , comprising: four sides (3, 4, 5, 6) defining an outline (2) , wherein the four sides (3, 4, 5, 6) comprise two major sides (3, 4) parallel to each other and two minor sides (5, 6) parallel to each other, characterized in that the outline (2) defined by the four sides (3, 4, 5, 6) is a chiral geometric figure such as not to be superimposable on its own mirror image.

2. Playing card (1) according to claim 1, wherein the minor side (3, 4) forms an angle (p) with the major side (5, 6) other than ninety degrees.

3. Playing card (1) according to claim 2, wherein: a. the angle (p) formed between the minor side (3, 4) and the major side (5, 6) is comprised between 89.3 degrees and 89.5 degrees; or b. the angle (p) formed between the minor side (3, 4) and the major side (5, 6) is comprised between 90.5 degrees and 90.7 degrees.

4. Playing card (1) according to one of the preceding claims, wherein the minor side (5, 6) extends from a first major side (3) to a second major side (4) along a direction not orthogonal to the two major sides (3, 4) and defines a maximum deviation (AL) from the orthogonal direction at the second major side (4) .

5. Playing card (1) according to claim 4, wherein the maximum deviation (AL) is less than or equal to 1 mm, in particular less than or equal to 0.7 mm, more in particular less than or equal to 0.6 mm, even more in particular less than or equal to 0.5 mm.

6. Playing card (1) according to one of claims 4 to 5, wherein a. the major side (3, 4) is comprised between 87.5 mm and88.5 mm, in particular 88 mm, the minor side (5, 6) is comprised between 62.5 mm and 63.5 mm, in particular 63 mm and the maximum deviation (AL) is 0.7 mm; or b. the major side (3, 4) is comprised between 88.5 mm and89.5 mm, in particular 89 mm, the minor side (5, 6) is comprised between 56.5 mm and 57.5 mm, in particular 57 mm and the maximum deviation (AL) is 0.6 mm; or c. the major side (3, 4) is comprised between 83.5 mm and84.5 mm, in particular 84 mm, the minor side (5, 6) is comprised between 54.5 mm and 55.5 mm, in particular 55 mm and the maximum deviation (AL) is 0.5 mm.

7. Playing card (1) according to one of the preceding claims, wherein the outline (2) is a rhomboid parallelogram.

8. Playing card (1) according to one of the preceding claims, wherein the outline (2) is a parallelogram with chamfered corners .

9. Playing card (1) according to one of the preceding claims, comprising a front face (7) and a rear face (8) , wherein: a. both the front face (7) and the rear face (8) are unprinted blank faces; orb. both the front face (7) and the rear face (8) are printed faces; or c. one of the front face (7) or the rear face (8) is an unprinted blank face and the other is a printed face.

10. Playing card (1) according to one of the preceding claims, further comprising at least one recess (10) along one side (3, 4, 5, 6) of the outline (2) .

11. Playing card (1) according to claim 10, wherein the two major sides (3, 4) each comprise a recess (10) .

12. Playing card (1) according to one of claims between 10 and 11, wherein the recess (10) extends internally to the card (1) with a maximum depth d3, wherein d3 is comprised between 0.65 mm and 0.75 mm, in particular 0.7 mm.

13. Playing card (1) according to one of claims between 10 and 12, wherein the recess (10) has a maximum extension dl along each of the two major sides (3, 4) , wherein dl is comprised between 19 mm and 21 mm, in particular 20 mm.

14. Playing card (1) according to one of claims between 10 and 12, wherein the recess (10) is located at a distance d2 from a corner of the card (1) , wherein d2 is comprised between 19 mm and 21 mm, in particular 20 mm.

15. Deck of cards comprising a plurality of playing cards (1) according to one of the preceding claims.

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