363 



VIETA, FRANCIS. 



VIETA, FRANCIS. 



3C4 



What more we have to say of Vieta must appear in connection with 

 his friendships or his writings. He died at Paris in 1603, according 

 to De Thou : Weidler says December 13, but without stating from 

 whence. Of his attachment to study the former writer says it was BO 

 excessive, that he often continued for three days together, fixed in 

 thought, without stirring from his chair, or taking more sustenance or 

 sleep than nature absolutely required. In religion he appears to have 

 been a zealous Roman Catholic, at least towards the end of his life, 

 and in politics a confirmed believer in the divine right of kings. The 

 assassination of Henry III. seems to have dwelt upon his mind for 

 years, BO much as to force him to recur to it in his writings, in places 

 where political allusion is a curious kind of digression. Thus, at the 

 end of his ' Responsa Mathematical published in 1593, he suddenly 

 breaks off from the subject of the Calendar to refer to that event, 

 which took place in 1589: 'Sed de iis tollendis ad ecclesiasticos re- 

 feram commodiore loco, ac ipsis detegam periodum qua) summo ipso- 

 rum applausu mirum solis et lunse consensum prodat fls Itpa i-iti^via.. 



Sed, 



" Eheu ! quis unctum eliminate mystico 



Necarc rcgem, sacrilega manu, 



Ausus cucullatus sodalis 



In numerum colitur Deorum ! 

 " Pii baud vacillent, KCCE MAI.TJS uosis. 



Tremant procaees, ECCK BONUS MAI.IS 



Non computer nomen soduli 



Omen at imposuit ncfamlo." 



The allusion in the verses is to Jacques Clement, who after the assas- 

 sination of the king, was considered as a saint by his party. 



This article is the proper place of reference to two minor mathe- 

 maticians, who are hardly' worth separate articles, but who owe some 

 of their fame to their connection with Vieta : Adrian van Roomen, 

 and Marino Ghetaldi. 



ADRIAN VAN ROOMEN, commonly called ADRIANUS ROMANTJS, was 

 born at Louvain, September 29, 1561, and died May 4, 1615 (1625 ?). 

 He published various works, of which the names may be found in 

 Vossius ' Do Scientiis Mathematicis.' The story of his acquaintance 

 with Vieta is told by De Thou, but more in detail by Tallemant des 

 Rdaux, whose ' Historic ttes ' (written before 1657) were published at 

 Paris in 6 vols. 8vo, 1834-35. In his ' Idea Mathematics,' &c., 

 Antwei'p, 1593, Romanus proposed a problem to all the celebrated 

 mathematicians whom he knew by reputation, naming them, but 

 without a Frenchman among them. Shortly after, the ambassador 

 of the States being at Fontainebleau, in conversation with Henry IV., 

 who was enumerating to him the celebrated men of the country, said, 

 "But, Sire, you have not a mathematician, for Adrian van Roomen 

 does not name one Frenchman in his list." " Indeed I have, though," 

 answered the king; "and au excellent one let some one call M. 

 Victe." Vieta came, was presented to the ambassador, who gave him 

 Van Iloomen's problem, placed himself at a window, and, before the 

 king left the room, wrote two solutions with a pencil. In the evening 

 he sent several others, offering more, as he said the problem was 

 capable of any number. Van Roomen, immediately on hearing this, 

 set off to Paris to see Vieta, followed him to Foiitenay, and spent 

 some weeks with him. We shall see more of his problem presently. 

 Tallemant, who was evidently not a mathematician, tells us the sort 

 of impression which Vieta's writings had created about the middle of 

 the 17th century. He says that this M. Viete, who had learnt 

 mathematics by himself, there being nobody to teach him in France, 

 wrote treatises so difficult that no one of his age could understand 

 him ; that one Lansberg, if he mistakes not (but he does mistake), 

 first deciphered some of them, and that since his time people had 

 made out the rest. It is worth noting that this same Tallemant is a 

 witness independent of De Thou ; for he informs us that Vieta died 

 young, of study, whereas, had he seen De Thou's account, he would 

 have found in the very first words that Vieta died "anno climac- 

 terico." And yet Alexander Anderson, who must have known his 

 friend's age, calls his death, " fatum immaturum." 



MARINO GHETALDI, of Ragusa, was of a good family, but of his life 

 we can find nothing; nor of his death, except that it took place 

 before 1630. Tallemant, already cited, says that a Raguean gentleman, 

 called Galtade (Ghetaldi), procured himself to be made minister of his 

 native republic in France, that he might have the acquaintance of 

 Vieta. Ghetaldi, in the letter already alluded to, says he was at Paris 

 on his own affairs when he first met with Vieta. The works of 

 Marino Ghetaldi are 1, ' Nonnullse Propositiones de Parabola,' Rome, 

 1603; 2, ' Promotus Archimedes,' Rome, 1603, a work on specific 

 gravities, which is sometimes cited on matters of weights and mea- 

 sures; 3, ' Apollonius Redivivus,' Venice, 1607; 4, 'Supplernentum 

 Apollonii Galli,' Venice, 1607, in continuation of the tract of Vieta 

 presently mentioned ; 5, ' Apollonius Redivivus' (the second book), 

 Venice, 1613; 6, ' Variorum Problematum Collectio,' Venice, 16U7; 

 7, ' De Resolutione et Compositione Mathematica,' folio (all the others 

 being quarto), Rome, 1630 (posthumous). There is not much of algebra 

 in Ghetaldi's writing-, but what there is comes from the school of Vieta : 

 the author so far bears out Tallemant's story, that he speaks of -his 

 intimate friendship with Vieta at Paris. Alexander Anderson (born at 

 Aberdeen in 1582), who taught mathematics publicly at Paris, was the 

 editor of two of Vieta's works, which came into his hands, one from 



the author, the other from his executors, as will presently appear. 

 [ANDERSON, ALEXANDER.] Nathaniel Torporley may also be named in 

 this connection, he having for several years acted as Vieta's ama- 

 nuensis. [ToRPORLEY, NATHANIEL.] 



It may perhaps save some bibliographical student a hunt for an 

 imaginary work of Vieta if we mention here the ' Supplemeutum Fr. 

 Vietae, ac Geometria) totius Instauratio,' Paris, 1644, by A. S. L. 

 This A. S. L. is Antonio Sanctini of Lucca, who had a few years 

 before published ' Inchnationum Appendix,' &c., with his name. At 

 the head of his dedication he calk himself Cwistantius Silanius Nice- 

 nun which is an anagram for Antonius Sanctinius Lucenxis. The work 

 itself is an impudent attempt to connect Vieta's name with pretended 

 solutions of the problem of two mean proportionals, the multisection 

 of the angle, &c. Both Sanctini's works were answered by P. P. Cara- 

 vaggi of Milan, in his ' In Geometria, &c. Rimae detecta?,' &c., Milan, 

 1650. Sanctiui's algebra is of the school of Vieta. It is a striking 

 corroboration of what may be suspected for other reasons, namely, 

 how little Vieta was appreciated in France for many years after his 

 death, that of all the persons we have mentioned as connected with 

 him, not one is a Frenchman ; but nevertheless some part of his works 

 was translated into French by one Vaulezard : we know that thia 

 translation exists, but we cannot find any mention of it. 



The writings of Vieta are rendered difficult to read by the then 

 almost universal affectation of forming new terms from the Greek, 

 and of introducing phrases in that language. His pages may remind 

 the reader of the English fashionable novels of twenty years ago, which 

 required a continual insertion of French words and sentences. Thus, 

 in the isagogc, we find zetetic, poristic, and eregetic processes, the first 

 consisting of antithesis, hypobibasm, and parabolism ; and also that by 

 an additional axiom, ' cuTi)fj.a non Suar/j.'fixavov,' many problems hitherto 

 ' &\oya,' may be solved ' fvrfx vus ' He uses the signs -J- and , and 

 also that for division ; but when he would designate the difference of 

 two quantities of which the greater is unknown, he places between 

 them our modern sign of equality, thus, A = B. The exponents are 

 expressed by words, either full or contracted ; and the numerical 

 coefficients are written after their accompanying; letters. The analogy 

 between algebra and geometry, which gave the name of square and 

 cube to the second and third powers is extended to all symbols. Thus 

 the equation 3BA 2 DA A 3 = Z, would be written 



B 3 in A quad. D piano iu A A cubo equatur Z solido. 



Here D is called D planum, and is considered as the repi-esentative 

 of a geometrical superficies, that the second term may be homogeneous 

 with the first : for a similar season Z is Z solidum. And in various 

 places it is expressly laid down, that it is not allowable to compare 

 quantities which are not thus rendered homogeneous. The great 

 difference between the methods of Vieta and of his predecessors is 

 one in which lies much, if not the greater part, of the power of 

 algebra : he was the first who used letters to signify known or deter- 

 minate quantities, and he was the first who systematically combined 

 the use of symbols of quantity with that of symbols of operation. By 

 this method the comprehension of a process which expressed in words 

 would be long and complicated, does not cost the practised eye a 

 second glance. It is true that the operations of those who preceded 

 Vieta would lead to a correct numerical result in any particular case ; 

 but the result only appeared, and the modus operandi was either lost 

 or wrapped in the dusky folds of a verbal rule. The notation of 

 Vieta expresses at once the rule and the result, and is a step in the 

 advance of science which, for the magnitude of its consequences, 

 deserves to be ranked with the invention of fiuxious. There is much 

 truth in the remark of Vieta upon his predecessors : ' Vovebant Heca- 

 tombas, et sacra Musis parabant et Apollini, si quis unum vel alterum 

 problema extulisset, ex talium ordine qualium decadas et eicadas 

 ultro exhibemus, ut est ars nostra mathematum omnium inventrix 

 certissima." 



We now proceed to a short account of the writings of Vieta, 

 referring for more detail to the second volume of Hutton's tracts. 

 Vieta, as we have said, printed his works privately, and we are not 

 wholly able to recover the dates of the several first publications. 



[But we put this paragraph in brackets, as we first wrote it, for a 

 reason afterwards mentioned it is not noticed that many of these 

 works, which are now only known by the edition of Schooteu, were 

 published together, or at least preceding publications were joined 

 together in one, by Vieta himself, before the year 1591, under the 

 name of ' Restituta Mathematica Analysis, seu Algebra Nova." Neither 

 Moutucla, nor any other modern writer that we have seen, appears to 

 be aware of this fact : the French historian does not seem to know 

 that the first seven books of the 'Responsa Mathematica,' of which 

 (i. 578) he regrets the loss, were contained in the collection alluded to. 

 The fact is nevertheless certain, as the following editions of different 

 separate works viz., 'In Artein Aualyticam Isagoge,' Tours, 1591; 

 'De Numerosa Potestatum ad Exegesin Resolutione,' ParL*, 1600; 

 and ' Supplernenturn Geometria),' Tours, 1593 contain in their title- 

 pages the name of the source from whence they were taken, and the 

 first of them also gives a list of the contents, from which list we have 

 placed II. M. before the titles of the following descriptions, in every 

 case in which the ' Restituta Mathematics ' is said to have contained 

 the work. Besides these, we must reckon among the contents the 



