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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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De Aneulo contacins.
CAP. 9.
eia FR, dMeCIUM D A P non divicac, nihil ek quod lundcat
hocmasislieri volle ver aliam quamris curram.
3. Consactus circulorum exierior, guantitas non est. C Um enir
nEC E A P, neC C A P, SIE quancicas, (Per praced) nequ erit
E A C quancicas, corum scilicer aggregarum.
4. Anouli qui fiunt a diametro es peripherid, sive intra sive exetre
circulum, recti funt, es rectis rectilineis equales. Nam, cum D A F
non lic quancicas, erune anguli D AC, D AH, aequales rectio
rectilineis P A C, P A K.
Hxec Theoremara, exillo Lemmate concesto, lac evidenti
consecutione inferri, non negat Clarius, neq; alii credo nec
bunc. Toca lis est de vericate iltius Lemmatis; An Scilicet Aneuti
similium segmentorum, salrem semicirculorum, sint aequaes. HlOC C la-
vius nexac. Videamus igirur quid in illius detentionem addues
PO(TIE.
Ouid autem ipse Pelecarius adduxit in ejus ad versus Clavi-
um Apologia, nescio quidem, quoniam illam Avologiam non-
dum inihri concisie videre. Ae in ipsius commencario quodam
De contactu linearum, (ebi eadem Fere habeneur qua ee in com-
mencariis ejus in Fuclidem ad 16 c3, cum aliqua tamen acccl-
lione,) nonnulla protere, quibus illius Lemmaiis vericauum ad
SEruere COnAEUE; Ouae mox examinabimus.
Pexmiccet autem, Hhoc pronunciatum, proprincipio Geometrico mo-
riio haberi pesse. P. E quidem mitii non iniguum videtur postula-
cum, ut concedatur; (quanquam non ignorem illua ob prX.
tentem concrovertiam, rix aliu quidem caula, in dubium voca-
ri.) Non enim eso omnino video, quo pacto tsura simles dici
voline, nisi ehomolosa lacera habeane provorcionelia, e I1
milirer ed invicem sica: AC, quonam pacto, qua angulos ina
quales Facieme, adcog; inz guales habent ad invicem inclinatio-
nes, incerim similicer lica dicancur, cgo prorlus non intet
liso.
In heuris rectilineis, nemo dubicar, variacionem anculorum
mutare speciem figurx, (non enim alicer differe Rhombus a
Oracraco:) Sc hxurarrm Epecie datarum angulos eriam daris
(per deE. 3. Dacorum Puclidis:) & quareillud in currilincie de
mistis feuris non cbrineret, nulla racio altignari pocest. A-
deoq; Cemicirculi, nih aequales habeans anguloss Agurx lirriles
dici non deberent.
LEbea