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# Title: Qua Continentur De Angulo Contactus & Semicirculi, Disquisitio Geometrica. De Sectionibus Conicis Tractatus. Arithmetica Infinitorum: sive de Curvilineorum quadraturâ, &c. Eclipseos Solaris Observatio (shelfmark Leibn. Marg. 84:2)
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ectoum nol
drithmetica insinitorum.
DROD. ZLV. Corollarium.
PrOP. 45
Inc discimus methodum inveniendi aream com-
plementi Parabolae, S. Paraboloideos Cubicalis,
Biguadraticalis. Surdesolidalis, aut superioris
cujustibet potestatis; e consequenter, etiam aream Pa-
rabola, ant Paraboloideos enjuscungi potestatis. Quod o-
stendere pollicitus sum ad prop. 48. Con. Sect.
Nempe, cum complementum Parabole (rel Semiparabola)
Eic Caries secundanorum, (uc diximus ad prop. 23;) comple
mencum Pacaboloidis cubicalis (vel Cemiparaboloidis,) le
rieo Terrianorum, (ac diximus ad prop 42;) alg; Ccedem ra.
cione) complementum Paraboloidis Biguadraricalis, seriet
Macinorum; complementum Paraboloidis Curde tolidalis, le
ries Ouimcanorum; ee sic dcincepo: Frit horum racio ad Paral
Lelosrammum circumscripcum, (Ceries nempe Locidem maxiu
mo aequalium,) ea qux cA 1 ad 3, 1 ad 4, 22d5, 72d 6, _ sc
scinceps: juxra cabellam propolicionis precedencis. F.F conte
quenter, ipla Parabola, Paraboloides Cubicale, Biguadracicale,
Surdelolidale, _C (quae nempe cum luis complemencis aquan-
cur Paralhelosrammis circum(criecis) lune ad Parallelosram
num circum fcriprum, uc 2. ad 3, 3 ad 4, 4 285, 52d6. &c.
SCHOLIVM.
Exhoc quidem pacto licebic intinicis fguris curvilineis Xqua.
les rectilineas constiruere. Ouodq: in Pol. Parabolo (lumma
cum admiracione) prasticic Archimedes (_ PoRillum alii;) id
nos in Paraboloide cujulcunq; poteltatis jam praesticimus.
Oux aurem de Parabolis _ Paraboloidibus huculq: eradica
Eune, aur etiam adhuc deinceps cradenda, possunc etiam Spirali-
bustacillino negocio accommodari. Si enim supponamus re.
ctam MT continue auseri, non quidem in eadem ratione cum
anguloPMT, (ur in Spirali Aechimedca,) sed in ejuldem raci-
one duplicaca, criplicata, quadruplicaca, _c. orientur alia 2193
alia Spiralium gener o: quarum camen ad peripheriam vel ar-
cum (co sentu quo dictum eA in Schol. prop. 13. d 15.) racto
BOA