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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)
# Folio 531, page id 851387705:0551
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nist
Tun
udi
a Y C F 0
proporcionales: Iiem rectae CZ. = 2 a Lig. 10. rectis B V LB, 7. FL Y
rectis 2 Y quadrantem Cib C complentibus proporrionales. Omnes isitur V Z ip
:sunc ut omnia rectangula VZ. XZ Y Ag. 7. Oux iterum in 2 a du-
Cae, sunc nchorum rectangulorum momenia respectu recta Bb fis. 7. Ouancum
aurem st horum omnium momencum sic colligimus.
66. Incellieatur primo super planum crilinet C. Z A F Fg. 7. erigi semicirculum
CBF ad anoulos rectos; ita quidem ut C F diameter Temicirculi, congruat C l
laceri crilinei. Deinde Super idem planum, moreri intelligatur idem semicirculus
inrariaro angulo, a C F ad CiB, et sic deinceps ulque ad A; hoc motu describens
Semiceylindrum: Duem Semieslindrum si secet planum rectae AC perpendiculariter
insistens, abscinditur semiestindei Portio (Tuper C A F criangulo jacens) ex inti-
nicis Paralselosrammis conslata, quorum bases intelligantur ordinarim applicata
in balis Semicxlindricae semicirculo, alcicudines arichmetice proportionales trian
sulum C AF complentes. Sin cundem semierlindrum secet superticies currata
perpendicularicer insiltens currae CZ A, abscindetur Semieslindri Frasmentum
Tsic enim, libet, distinctionis caula, vocare) Super CZ A F crilineo misto jacens
ex Parallelogrammis icem intinicis conslatum, quorum bales incellixantur caedem
2 L oedinacum applicala in temicireulo, alricudines vero LZ crilineum CZ AF
complentes.
67. Hlaec autem duo Colida, nempe Portio semiexlindri, plano abseilla, ee semi-
exlindri Frasmencum, absciltum superticie currata, sunt quoad magnitudinem in
ter se aequalia. (Propter, cum binas qualris rectas Z Y in base, utrinque a medio
aequaliter remotas, inricem aequales; cum binas ubique his balium rectis conoru-
entes alcicudines, sire in trilineo misto, sire in trianulo rectilineo, simul aequa
les rectae AP.) Vrrumris Eiquidem Semiestindro ejuldem batis, semialto, X
quale.
68. Sune autem eadem duo Colida, quoad momentum respectu AF recta, in-
regualia: Propter cranstatum id torum quod in alcero infistic bilinco, B A, ad si-
cum BC in reliquo.
69. F.I autem Portionis, crianeulo rectilinco incumbeneis, momentum respectu
AF recta, 3= D =~ 2 = = D F ZXS ∞. (FA enim CemicirculuS F BC =5D F
S Temialcicudo sA F = a P, adeoque porrionis magnicudo in D P=; qua in 87
distantiam CenCrI BraviCaLS ab A F (Det 557) ducta, dat 336 D = X 2 POrtio.
nis mOmEnCu.) Frasmenci vero, crilineo misto insistentis, momencum re-
spectu ejuldem A F rectae, est (per S+OS) 1 R24
R
D2 D
Unde h auteratur Porrionis momentum 356 EDE, habetur 356 2 P 2 = 3 D
momentorum ditterentia.
70. Pr contequenter (eum haec monencorum disterencia non aliunde provenin
quam ex segmenei bilineo BA insistentis in sicum BC traustatione,) li illa mo
mentorum disserentia incelligatur per magnicudinem cranstocatae parris divila, unde
habeacur mentura promorionis centri graricatis quancum ad AF rectam; hujus
que semissis, distantia utique ejuldem centri d Bb, in eandem magnicudinem ilerum
mulciplicata; prodibic Dividui semittis, nempe ,i D 2 p 2 = + Da, monientum
istius cranclocarae partis, bilineo BC intiltentis, respectu rectae Bb.
71. Deinde, super criangulo C. BB rectilineo, incumbit estindri quadrantalis
porcio, cujus balis C b C quactrans circuli, alticudo Bb = = P; momencum vero
ejuldem respectu recta Bb. est is D3 P =, i2 DE D2. Quod eodem modo collioi
Tux quo Supra (= 35 de segg. colligicur momentum ejulmodi portionis F L v
H8. 5. Cum enim illic = 39 habetur =, D + =, 8D. D momeni augmenein (ob
dictae portionis ibidem translationem) respectu recta P A, (si nempe incellisacur
YF A planum horizonti parallelum) vel rectae FP (B Seilicet planum Y F X ho
rixonti paralletum incelliratur:) Adeoque ejusdem lemiltis L ∞
6D3F, DOI
tionis dictae momentum respectu recta LZ vet Z. (prour haec vel illa incelligatur
horizonci parallela,) polita quidem (quod illie lupronitur) segmenci alcicudine
T0 = ZD: Onde, li posira tuistet XV = à P (Prour jam in eatu limili SupponiinuS
super aequalem balem porcionis alcirudinem Bb=
L) Fuisset ejusdem momentum
respectu rectae YZ ret Y on 56D3 P= si DEP: Ouod isicur est momencum por-
XX X 2
riOnIS