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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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864 PFOD. XXII. DeCalculo Contri Cravitatis.
Fix. 172. opposicarum balium superticiei istius Cencra gravicatis conjungis, per prop. 5. hu-
sus: Frgo, in hujus puncto medio
Adeoque, propter datum areus circularis centrum graritatis, per T4 hujus; da-
bitur, non tancum corius Iuxerticiei Curra Cylindri recti, led ex portionis cu-
jutris (duabus rectis ad batin perpendicularibus incerjocte) Ccirum gravi
EdLIS.
Idemque limiliter dabitur, in alia superticie columnari, etiamsi aA Z Curva, non
sic arcus circuli, sed alia quaris curra, dummodo hujus currae centrum graritatis
nocum (IL.
Si vero ex hujus Cytindri recti superticie curra, plano quovis T u A F uteun-
que oblique potico, abscindi incellisatur superticialis Onsula Pn A s; (ubicunque
concingat PA, Ongulx acies; non minus quam (i Sic Diameter Circuli Pd A:
proviei dacum inclinationis ansulum v a B, arculque Centrum sraritatis; dabitur
Onculx altieudo super cenerum illud, quae in arcus longimdinem ducta dat super-
ticialis iltius Ongula ATCaM; Der PrOP. TI. hujus. Ouod non minus valei de
Ongula FOTa Fu AS, quam de partialibus ABv, B0n S, eoc. Nam _ hic ob data
aECIUM AB, Bs, ecc. Centra graviratis, adeoque eorum ab acie A T distantias, et
angulum inclinationis, adeoque alcicudinem super gravicaris Cenera; habebitur
area; Ducta alcicudine illa in currae lonsirudinem.
Acque haec obcinene, quaecunque sit AdX curra (non minus quam si su arcus
circularis,) cujus de Lonsitudo ee Centrum gravicatis nota intelligantur.
Hlabicis aurem, eo quo dictum cMt modo, Onsularum magnicudinibus; carundem
Momenta ea mechodo inrestisari poltune, quam, ex prop. 10. peciram, in Luperio.
ribus Eaepius actibuimus: Nempe, omnium arcuum (Ungulam superticialem com-
plencium) Momenta respectu expolicae rectae, (quae, propter cognita curvarum
cum lonsuudines, cum Cenrra graricaris, adeoque iplorum ab expolita recta, pla-
nove per illam perpendiculari, distanas, habentur,) sune ipsum Ungulae Mo-
mencum respectu iltius rectae; quod, per magnicudinem diritum, extribet distan-
riam Centri graritatis ab illo perpenaieulari plano. Aique hoc si respectu plu-
rium rectarum (quae non sincad iuricem parallelae) tiac; habebicus iptum era
ricatis Centrum.
Vel etiam, (per SW. prop. L3. hujus) haberi poltune Ongularum iltiusmodi
in superticie Cxtindri recti, saltem quarum acies est Circuli diameter, Centrum
Gravitatis; ee Cytindracearum superticierum (parallelis rectis interjectarum) C’en
tra dari, modo oltensum est, SC, D, hujus: Aique in harum aliquas (addendo
vel subducendo, prout opus tueric,) resolri pocest iltiusmodi quaeris Ungula su-
perticialis Cytindri recti, (ut exemplismox proterendis oltendetur:) Dabitur isI.
CUIT, (Der PTOV. 27. Cap. praced.) istuismodi cujutris Ongula Cencrum gravicatis.
HaC autem, quo ad alias curras transterantur, OpuS Crit, ut cum ipliuS AS Y
quaecunque fuerie curra, cum parcium iptius qua rectis puta ipsi A P parallelis (si
nempe momencum respectu hujus inquiratur) aequalicer ab invicem dilticis abscin-
duncur, cum longitudines, cum Cenrra graricatis, vel (quae ex his retulcant) mo-
menta habeamrur. Ouippe, his tabicis, momenca similicer exquirentur (per PrOP.
20. hujus) acque si ellent arcus circulares.
Ouod aurem de Ungulis superticialibus tradicum est; idem ad quasris in Ca su-
18. 189. perticie tixuras, planorum uccunque politorum intersectionibus (cum ea curra su-
perticie) cerminatas, accommodabitur. Nam, uctigurx quaeris in plano rectili-
nea resolri pollime in rectansula criansula et parallelosramma; eodem tere modo
tigurae quaelibet (in recti Cylindri vel Columnaris solidi superticie) planorum
lectionibus factae, resolvi polline in superticiales Vngulas et Cy lindraceas superti.
cies rectangulas. Adeoque ex partialium magnicudinibus habiris, hrabebicur (ad.
dendo, et subducendo, uc calus poscularerie) magnicudo expolica: Aeque, ex illa-
rum habitis Ceneris praritatis, habebitur hujus, per proP. 27. Cap. praeccd.
Exempli gratia; Su iltiusmodi Fieura expolira (’in superticie Cylindei recti)
planis terminata, C AD, (ti8. 189.) Acque deistis (ad Cylindri balin B AS)
rectis CB, DS; eric expolica C AD figura, eadem acque Ongula superticialis
CB ASD, dempris C AB, e D AS.
Sed, propter dari areus B AS Centrum graritatis datum (per prOP. T4. hu-
juS,) adeoque ipsius diltanciam d daca Ongula acic ( seu communi balis B AS,
planique Cnontam abscindencibus CD F, sectione) XL; e conseguenteT (PEOP
et