Re: [HM] 1554 Tartaglia

Prof. Lueneburg (luene@mathematik.uni-kl.de)
Thu, 10 Jun 1999 10:38:50 +0200 (MESZ)

Fred Rickey wrote on June 10, 1999 among other things:
>
> The 1554 edition of Tartaglia's
> Quesiti, et inuentioni diuerse
> is somewhat scarce. Only 11 copies are listed in the OCLC catalogue in US
> libraries. The Library of Congress has one, as do Columbia, Case, Brown,
> Harvard and Michigan. There are other editions: 1546, 1606, and a 1959
> reprint.
>
> Here at West Point we have an English translation from 1588:
>
> | AUTHOR: Tartaglia, Niccolo, d. 1557.
> | TITLE: Three bookes of colloquies concerning the arte of shooting in
> | great and small peeces of artillerie,
> | ... Written in Italian ... now translated into English by
> | Cyprian Lucar ... Also the saide Cyprian Lucar hath annexed ...
> | a treatise named Lucar Appendix ... to shew ... the properties,
> | office and dutie of a gunner ...
> | PLACE: London,
> |PUBLISHER: [Colophon: Printed by Thomas Dawson] for John Harrison,
> | YEAR: 1588
>
> but I have never looked at it. But I think I shall. This, as well as almost
> any early English work, is available on microfilm. [Aside: I took an
> interest in this question as I was working today on a bibliography of the
> 1340 pre WWI volumes in the West Point Library that will be published by the
> AMS; this Tartaglia will NOT be listed as it does not contain a sufficent
> amount of mathematics.]
>

But it contains substantial mathematics:

Quando chel cubo con le cose appresso
Se agguaglia a qualche numero discreto
Trouan dui altri differenti in esso.
Da poi terrai questo per consueto
Che'llor produtto sempre sia eguale
Al terzo cubo delle cose neto,
El residuo poi suo generale
Delli lor lati cubi ben sottratti
Varra la tua cosa principale.
In el secondo de cotesti atti
Quando che'l cubo restasse lui solo
Tu osseruarai quest'altri contratti,
Del numer farai due tal part'a uolo
Che l'una in l'altra si produca schietto
El terzo cubo delle cose in stolo
Delle qual poi, per commun precetto
Torrai li lati cubi insieme gionti
Et cotal somma sara il tuo concetto.
El terzo poi de questi nostri conti
Se solue col secondo se ben guardi
Che per natura son quasi congionti.
Questi trouai, & non con passi tardi
Nel mille cinquecente, quatroe trenta
Con fondamenti ben sald'e gagliardi
Nella Citta dal mar'intorno centa.

Quesito XXXIII

And they contain also Tartaglias view of his quarrel with Cardano.

For those who know German better than Venetian, here my translation of the
above poem.

Wenn der Kubus mit den Cossen daneben
gleich ist einer diskreten Zahl,
finden sich als Differenz zwei andere in dieser.
Dann halte es wie gew"ohnlich,
dass naemlich ihr Produkt gleich sei
dem Kubus des Drittels der Cossen,
Und der Rest dann, so die Regel,
ihrer Kubusseiten wohl subtrahiert
wird sein deine Hauptcoss.
In dem zweiten von diesen Faellen,
wenn der Kubus alleine steht
und du betrachtest die anderen zusammengezogen,
Von der Zahl mache wieder zwei solche Teile,
dass der eine in den anderen multipliziert
den Kubus des Drittels der Cossen ergibt.
Von jenen dann, so die gemeine Vorschrift,
nimm die Kubusseiten zusammen vereint
und diese Summe wird dein Ergebnis sein.
Die dritte nun von diesen unseren Rechnungen
loest sich wie die zweite, wenn du wohl beachtest,
dass sie von Natur aus gleichsam verwandt sind.
Dieses fand ich, nicht schwerfaelligen Schritts,
im Jahre tausenfuenfhundertvierunddreissig
mit Begruendungen triftig und fest
In der Stadt vom Meer rings umg"urtet.

Heinz Lueneburg