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# Title: De Locis Solidis Secunda Divinatio Geometrica (shelfmark Leibn. Marg. 151)
# Folio 155, page id 898203430:0183
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GRDIHATIONVM COMC. LIMITIBVSLIB. I.
I
n
1L L se.
a
Vcusque absoluram exhibuimus doctrinam de LDCISSOLIDIS, quo ad
Orainationem ramorum ab orieine interna, vel externa vbicunque da-
ta in qul tam Circun, quam Parabola, vel in axe transuerso, aut conivea
10 Fipsis, vel  sive etiam opposirarum sectionum. Verum enimue–
ron quoniam (vi in secacesima octana provosirione Libri y. primae nostrae
Divinat. in apollontum opporiune monuimus) anculus rectilineus quicunque
haberi pores hanquam Hyperbola omnium similium; es concentricarum angu-
sissima, seu tanquam prima, ac minima earum; quibus communis sit AnEu-
lus asympotalis. curus semiaxis transuersus abit in punctum, in ipsum
nempe verticem anguli ejusdem; hunc itaque aneulum huc quoque, veluir Co-
nicam sectionem considerabimus, ex quidem haud inconsulio, quaecunque
enim sectio coni, basim habentis, per verricem ducta, triangulum exhibet
in ipso Cono; in Coni vero superficie angulum rectilineum; super quam, per
plana quaelibet ipsius ansuli plano parallela, destenantur yperbolae omnes inier
se similes, quarum communis sectio cum plano per axem ducto, (Ut requiri-
cur in xij. primi Conic.) convenit cum viroque latere eiusdem trianouli per
axem eodem penitus modo, quo communis sectio plani in quo est ansulus,
eidem per axem plano occurrit. Duapropter Limitem quoque Ordinationis
ramorum ab orieine interna, vel externa vbicunque data in anguli avc
nempe in recta illum bifariam secante, apud alios Limites huius quariae Par-
tis apponere visum est, atque ila eidem Parri finem imponere, ve in sequen.
PROPOSITIO LXXZ.
N Anculo rectilineo. Limices Ordinationis ramorum
ab orieine interna, vel externa ductorum; sunt ad
conuexa earundem Sectionum oppositarum inaequalium
laterum, (5 anculi latera tancentium ad terminos or-
dinatae per orieinem, a qua ipsarum centrum distat per
altitudinem rami minimi, semiaxis vero transuersus
ipsi minimo ramo aequalis est, atque ad suum semire-
ctum latus est ut semiordinata ex orisine ad amplitu-
dinem rami minimi.
IT Angulus rectitincus ABC, cuius axis B D vicunque productS,
DCrque data prius intra angulum oriso quaecunque D, à qua ducei sInE
minimi ramis seu perpendiculares DP, DF Tuper latera BA, BC, qui,
ve constat, inter le aequales crune; per D vero lic ordinata A D C, iun
SatUEque P. F, quae ipsi AC requidistabic; nam in criangulis F DO, FDO
anguli ad D sune aequales, (co quod et ansuli adt B in trianeulis reCtAN-
Sulis