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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 714, page id 851387705:0734
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De Calculo Centri Cravitatis.
CaP. V.
iptis B, D, punctis constitura, ab axe convertionis X diltabune respectirorum ar.
cuum Semidiametris ZB, Z D. Iplorum vero Arcuum lingulorum (Rectis aequa-
lium, ec inricem similium,) Centra graritaris (Proprer curvationem) in eadem
ratione omnia (propter arcus similes) propius admorentur ad conrertionis Axem
Z: atque in eadem ratione minuirur Niomencum (respectu ejusdem X axis) sin-
sulorum; adeoque e simul omnium; e propterea, communis omnium C’entri
gravitacis distancia. Nempe (per modo demonstraca) uc Arcuum unus quilibet
bBb, ad bb Chordam Cuam; lic Distancia Ceneri graricaris, adeoque Momencum
cum lingularum, cum limul omnium, Rectaram BB, SS, _c. Ongulam complen-
eium; ad Distanciam centri graritaris, de momentum, cum lingulorum respectire,
cum simul omnium, Arcuum bBB, dDd, Ecc. (Superticiem Solidumre conrer-
Tione circa Z Factum, complentium,) ab eodem X convertionis AXC. PUTa, ut
ArCuS a, ad Chordam 5; siC X C dictancia illa, ad diltantiam hane X3. Quod item
demonstrandum Crat.
FocelL; In Semi convertione; uc Z P ad Z R: seu nt P ad 4 R.
Porro: Cum oltensum sic (ad 5. L. Prop. praeced. ). In portione Sphaericae Su-
perticiei incegrae, parallelis planis interjecta (quam Zonam inteeram apDello,)
DUTa, QuIA ArCUS F. C circa B F convertione inceora deseribitur; Cencrum orari
tatis esse in Axemedio, (puta, in rectae BF puneto medio:) Adeoque in Zonis
imperfectis, (puta, quae converlione dimidiata, aliave impertecta, deseribuntur,
E correspondentibus Ongulis; Concrum Graritatis in eo plano elié, quod tancun-
dem dister a plano sphaeram in e. rangence, seu quod mecium eAt incer B d P
axi rectum.
Sique (Per prOP. 12 tnjus) in illo plano quod (per convertionis AXem vel
Ongulx Aciem A a incedens) bisecar, in superticie Ongulari, crectas omnes re
ctas illam constituentes; in Sphaerali, omnes Areus convertione Factos: Ouippe,
in quo Plano Tunc Omnium Centra srariraris, in eodem est commune omnium.
Duod autem rectarum illarum unam bilecat, bisccat omnes; arcuumque unum
bilecans, omnes bisecat: propter similia illic Friangula, hic Arcus similes; ob
eundem Inclinationis Angulum ad Aciem vel Axem A a: ) Adeoque in duorum
illorum Planorum communi sectione:
Ouo ipsum Centrum decerminetur (in Ingulis hisce, de Zonis impertectis,
Ouaerenda erit etiam ejusdem (in hoc plano per Aremrranseunte) diltantia ab
ACIC vel AXC Aa Onod SC BabCTUE.
Incellivatur Areui cuiris, uE F E, insiltens semiquadrantalis Ongulae (aciem
habentis BP) Superticies Curra: cujus lingulas rectas arcui insistences (superti-
ciem curram complentes) aequales else respectiris Sinibus rectis (ad 5. 1. prop.
Praced.) ostensum est; (adeoque superticiem illam Summa Sinuum aequalem; hoc
elt Facto ex AIcicudine BF, quam ldicamus, in Radium ducta; hoc clt, lR; per
S. LV. PrOP. Praeced.) Sed carundem distantia a perpendiculari plano per aXeM BF.
Tunc item iidem sinus recti. Momenta itaque singularum (magnicudine in di-
stantiam ducta) sune ut Sinnum Guadrata. Adeoque omnium Momenca (respe.
dtu rectae BF) uc omnia s. Tumma Ouadratorum Sinuum. HJoc est (Der S. V
ejusdem) ut spatium F B F G in Radium ductum. Ouod quidem spacium RBFC
(cum latis innoteseat) dicamus k2; adeoque k R est Momentum expolix super-
ticiei currae Ongularis, respectu rectae BF. AIquC hOC MOmentum Per Magnicu-
dinem IR diritum; exhibet =,  -  distantiam Cenri eravicacis à perpendieu.
lari Plano Tuper A a crecto.
Cumque eadem Tirratio (hoc respectu) Ongularum cujuscunque sinc Alcitdi-
nis; (urcunque enim auela Alcicudine, adeoque e Magnicudine, et Womento; puta
in ratione P ad R; exic adhuc eadem diltantia; J4
IR = 7: ) Erit cujuF
cunque superticiei Ongularis, suver Arcum Circuli crectae, (Aciem habencis
Circuli Diamerrum Ae) Distancia Centri graricatis a perpendiculari plano per
ipsam Aa, =; hoc est, quae oritur ex plano F. B F C ad rectam B F axplicaco.
Fademque cAet, (dempra curvitate, quae convertione Dritur,) in Superticie
conrextione facta, a convertionis Axe diltancia; (proprex tingulos Arcus in hac,
tingalio