Benedetti, Giovanni Battista de, Io. Baptistae Benedicti ... Diversarvm specvlationvm mathematicarum, et physicarum liber : quarum seriem sequens pagina indicabit ; [annotated and critiqued by Guidobaldo Del Monte]

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420408IO. BAPT. BENED. 18. puncta rectangula, hoc eſt vna vncia cum .6. punctis rectangulis. Deinde ex
multiplicatione vnciarum .2. ſecundi lateris, cum .3. trabuchis primi lateris, produ-
centur .6. vnciæ.
Ex multiplicatione poſtea dictarum .2. vnciarum ſecundi lateris
cum .2. pedibus primi, producentur .8. puncta.
Demum ex ijſdem .2. vncijs ſecundi lateris cum .3. primi, producentur .12. atto-
mi, ideſt vnum punctum.
Quæ omnia collecta facient trabucha .8. pedes .3. uncias
2. & attomi .3. omnes rectanguli oblongi.
Pulcherrima profecto operatio.
Trabucha. pedes. vnciæ.
3. 2. 3.
2. 3. 2.
6. 4. 6.
1. 3. 1. 6.
1. 6. 8.
1.
8. 3. 2. 3.
Videamus nunc exercitij cauſa, vt dixi, quomodo conueniat calculus iſte cum
calculo ordinario communi?
Nam quotieſcunque dicta latera, fracta fuerint in vncias, primum latus erit
vnciarum .243. ſecundum autem .182. productum vero vnius in alterum erit vn-
ciarum quadratarum .44 226. quod quidem productum cum diuiſum fuerit per .
5184.
vncias quadratas vnius trabuchi quadrati, prouentus erit .8. trabucho-
rum, reliquus verò numerus, ſiue fractus, erit vnciarum quadratarum .2754. qui
cum diuiſus fuerit per numerum .144. vnciarum vnius pedis quadrati, prouenient
pedes .19. quadrati cum vncijs .18. ſuperabundantibus, dicti autem pedes .19. ſignifi-
cant tres pedes rectangulos oblongos cum vno pede quadrato, hoc eſt cum duabus
vncijs rectangulis oblongis, vt ſupra.
Videndum nunc eſt, vtrum illæ .18. vnciæ æquipolleant tribus punctis rectangu-
lis oblongis:
ſed hoc manifeſtè videre eſt, ex hoc, quia quęlibet vncia rectangula
oblonga componitur ex .72. quadratis, punctum autem rectangulum oblongum, cum
ſit duodecima pars ipſius vnciæ rectangulæ oblongæ, ipſum componetur ex .6. vn-
cijs quadratis .18. igitur vncijs quadratis, triplum erit ipſius puncti rectanguli dicti.
Vnde clarè patet, quod, quotieſcunque voluerimus ſcire proportionem ipſarum vn
ciarum quadratarum ſuperabundantium, ad punctum rectangulum oblongum, ſi
dixerimus ex regula de tribus, ſi .72. (vncia rectangula oblonga) dat .18. quid dabunt
12?
puncta rectangula oblonga, quarum vnaquæque eſt duodecima pars ipſius vn-
ciæ rectangulæ oblongæ, in præſenti autem caſu prouenient .3. pro quarto termino
quæſito, & habebimus propſitum.

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