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# Title: [Johannis Wallis S. T. D. Geometriae Professoris Saviliani, in Celeberrima Academia Oxoniensi; Opera Mathematica] Johannis Wallis S. T. D. Geometriæ Professoris Saviliani, in Celeberrima Academia Oxoniensi; Opera Mathematica (shelfmarks Leibn. Marg. 100:1/2, Stück 1; Leibn. Marg. 100:1/2)
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MULTTPEECATIONE Cap. XXII.
libet, dux recta, quarum altera st trium, altera quatuor pedum, (vel palmo.
rum, calamorum, orsriarum, spichamarum, aur quarumliber aliarum menlurarum
aequalium.) Rectanguli magnitudo lire area repericur duetu linearum unius in al-
reram, lonsitudinis puta in lacicudinem, vel contra: eodem plane modo quo toti
dem numerorum series essent computanda. Si enim, verbi gratia, cor puneta,
vel (si liber) cor milites ordinarim digesti, ea lese disponaneur,
uc, in qualibec serie cransversa, quarerni, in qualibet directa,
cerni conspiciantur: maniteltum Cs ter quaternos, vel quater
cernos, ita ese dispolitos. Mulciplicatis isitur 4 Der 3; vel 3
DET 4, CMETSCE OMMIU nUMeTUS 12 = 3X 4. EF Parirer in li-
mili quaris cujutris numeri dilpositione taciendum exir.
Fodem modo Parallelogrammum 3 Dedes lacum, Xc q pedes lonoum, ex ductu
laticudinis in Lonsitudinem, reperietur pedum quadraticorum +2 = 3x 4. Cujus
quidem rei ratio lic facile percipietur. Si enim parallelogram.
mi iltius tam aleitudo sire lacieudo A, pedum crium, quam ba(IS
lirelonsitudo, pedum 4, diridi incellisantur in luos respe
ctire pedes; atque à cujusque pedis termino ducaneur rectae
lateribus parallela, quibus cora ligura in particulas quadratzs
dirimatur, quarum quaelibet sic tam longa quain laca pedem v-
num, (hoc elt, quaeliber concineat pedem quadratum;) mani-
Feltum eric, ex ip(o Schemaris inspectu, in qualibet serie tranlverla (propier lon-
sicudinem quatuor pedum) quatuor quadracicos pedes concineri, iplalque series
(propter alcicudinem erium pedum) numero rres elle; adeoque pedes quadraricos
omnes esse ter quaternos, hoc elt 12 = 4. X3. Ec quidem, pari ratione, manite.
Ium erit (propter A = 3) lingulis seriebus crectis eres pedes quadraticos contis
neri, ipsalque series (propter B = 4) numero quatuor; adcogne pedes quadrari-
eos omnes esse quater ternos, hoc clt 12 == 3X 4. Ec similiter in aliis quibulvis
Parallelogrammis rectangulis mensurandis (Cire quadrata line sive oblonea) ex
ductu. lonsitudinis in lacicudinem, (lire quod cantundem valer) basis in alcitu.
dinem (vel hujus in illam,) habetur area.
Atque hinc collipere licet, Pedem quadraticum unum, continere Dieitos sive
Oncias, 244. Cum enim longicudo Pedis unius sIE unciarum (2; Ft propterea PC-
dis quadraciei tam lonsicudo quam lacicudo sIE X2 unc. ex ductu hujus in illam
eerGIE areA T2X T2 = 244 unciarum quadraricarum. Adeoque, ueut pes linealis
contineat non nili T2 unetas lineales; pes tamen quadratieus continet uncias qua-
draricas r44. Fodem modo cum apudnos communis Virea mensoria officinarum
(a Tard dicta) contineat loncitudine pedes tres; eadem mensura
quadratica continebit pedes quadraticos d == 3X3.
Flaec Si per Cymbola libeat explicare; pro latitudine seu alcitu-
dine ponatur A, pro lonsicudine seu bali B; erit igitur Area seu
magnicudo AB, sive A X B. Ergo ( A = 3, e B = 4, crit AB =
A A = A 4. Aceoque, cum lonsicudo pecis unins sIc LZ UnCIaFUM; eC PFOPICTCA
F
T
= P 4 = 24+VV = 244V9
pedis quactraniet tam batis quam alcicudo +2 unc: ideoque A B = P P = P g =
12VX FZV = +44SV = 244V9. HIOC CH, P9=144V9.
vel unus Des quacraricus aequalis 244. Oneiis quadraticis.
Et eodem modo, in Virga quadrarica, cum tam batis quam
alticudo Sic Dedtum 3, cric area V g = 9P9. Et simili.
tex alibi.
Hlac methodo, in mensurandis, rerbi graria, assereutis
lieneis; _ Alseris unius lacitudo A Cit duum Dedum, longi-
cudo B pedum 20; critarea sive magnicudo AB = 40 P9;
hoc elt pedum quadratieorum quadraginta.
Similiter, Si Camera mensuranda lie lonsa pedes 18,
taca peces 22, erir cocius area leu magnindo, pectum
GlauiraLICONIM 216 =- 12X 18.
Pariter,
+
=1
d