462442GEOMETRIÆ
poſitæ ex dictis trapezijs, &
triangulo, FIQ, quæ oſtenſa eſt eſſe
minor ſpatio reſiduo iam dicto circuli, ECDB, & ideò figura com-
poſita ex dictis faſcijs erit minor ſpatio reſiduo iam dicto, cuita-
men circumſcribitur, quod eſt abſurdum, non eſt ergo trilineum,
FLHG, minus dicto ſpatio reſiduo circuli, ECDB, & oſtenſum eſt
neq; eſſe illo maius, ergo erit illi æquale, & triangulus, FHG, eſt
æqualis circulo, ECDB, ergo triangulus, FHG, ad trilineum,
FLHG, erit vt circulus, ECDB, ad reſiduum ſpatium ab eo dem-
pto ſpatio ſub ſpirali, A53 MB, & voluta, AB, ſed triangulus, FH
G, eſt ſexquialter trilinei, FLHG, ergo circulus, ECDB, erit ſex-
quialter ſpatij reſidui iam dicti, & conſequenter erit triplus ſpatij,
quod comprehenditur ſub ſpirali, A53MB, & voluta, AB, quod
erat oſtendendum.
minor ſpatio reſiduo iam dicto circuli, ECDB, & ideò figura com-
poſita ex dictis faſcijs erit minor ſpatio reſiduo iam dicto, cuita-
men circumſcribitur, quod eſt abſurdum, non eſt ergo trilineum,
FLHG, minus dicto ſpatio reſiduo circuli, ECDB, & oſtenſum eſt
neq; eſſe illo maius, ergo erit illi æquale, & triangulus, FHG, eſt
æqualis circulo, ECDB, ergo triangulus, FHG, ad trilineum,
FLHG, erit vt circulus, ECDB, ad reſiduum ſpatium ab eo dem-
pto ſpatio ſub ſpirali, A53 MB, & voluta, AB, ſed triangulus, FH
G, eſt ſexquialter trilinei, FLHG, ergo circulus, ECDB, erit ſex-
quialter ſpatij reſidui iam dicti, & conſequenter erit triplus ſpatij,
quod comprehenditur ſub ſpirali, A53MB, & voluta, AB, quod
erat oſtendendum.
_H_Inc patet eductas à vertice parabolæ ad ſecantem quamcunq;
diametro eiuſdem parallelam, parabola, ac tangente ibidem
interceptam, ſimiliter ſecare eandem, actranſiens per punctum cur-
uæ parabolæ, in quo prædicta eam diuidit, eidemq; parallela, ſecatip-
ſam tangentem, eſtenſum enim eſt, ex. g. HG, ad GΓ, eſſe vt, GF, ad,
FQ. ex quo nouus, ni fallor, ac pulcberrimus deſcribendi parabolam
elicitur modus.
diametro eiuſdem parallelam, parabola, ac tangente ibidem
interceptam, ſimiliter ſecare eandem, actranſiens per punctum cur-
uæ parabolæ, in quo prædicta eam diuidit, eidemq; parallela, ſecatip-
ſam tangentem, eſtenſum enim eſt, ex. g. HG, ad GΓ, eſſe vt, GF, ad,
FQ. ex quo nouus, ni fallor, ac pulcberrimus deſcribendi parabolam
elicitur modus.
_S_It deſcribendæ parabolæ diameter, A2, baſis, QX, cuiper, A, ſit
ducta parallela, LF, ſintque, AF, AL, æquales ipſis, 2X, 2Q, æ-
qualibus, ſecta autem, AF, in quotcunq; partes æquales, vt in quin-
que, velutietiam, LA, in punctis, K, I, H, G, B, C, D, E, per ipſa du-
cantur diametro, A2, æquidiſtantes, ΚΣ, 19, H8, G7, B3, C4, D5, E6,
ſecantes ſi niliter baſim, QX, in æquas partes in punctis, Σ, 9, 8, 7, 3,
4, 5, 6, tandem iunctis,, LQ, FX, ipſæ ſimiliter ſecentur ac, AF, vel,
AL, ſcilicet in quinq; partes æquales in punctis, R, S, T, V, M, N,
O, P, & ad bæc puncta ducantur ab, A, rectæ lineæ, AR, AS, AT,
AV, AM, AN, AO, AP, necnon, AQ, AX, notentur autem pun-
cta, in quibus eductæ ab, A, ſecant parallelas diametro, A2, eatamẽ,
in quibus eductæ diuidunt eas parallelas, quæ viciſſim abſcindunt de
ipſis, AL, AF, verſus, A, eandem partem, quam ab ipſis, QL, XF, ab-
ſcindunt eductę, verſus tamen puncta, L, F, vt ex. g. notabimus pun-
ctum, γ, in quo educta, AP, abſcindit {4/5}. ipſius, QL, verſus, L,
ducta parallela, LF, ſintque, AF, AL, æquales ipſis, 2X, 2Q, æ-
qualibus, ſecta autem, AF, in quotcunq; partes æquales, vt in quin-
que, velutietiam, LA, in punctis, K, I, H, G, B, C, D, E, per ipſa du-
cantur diametro, A2, æquidiſtantes, ΚΣ, 19, H8, G7, B3, C4, D5, E6,
ſecantes ſi niliter baſim, QX, in æquas partes in punctis, Σ, 9, 8, 7, 3,
4, 5, 6, tandem iunctis,, LQ, FX, ipſæ ſimiliter ſecentur ac, AF, vel,
AL, ſcilicet in quinq; partes æquales in punctis, R, S, T, V, M, N,
O, P, & ad bæc puncta ducantur ab, A, rectæ lineæ, AR, AS, AT,
AV, AM, AN, AO, AP, necnon, AQ, AX, notentur autem pun-
cta, in quibus eductæ ab, A, ſecant parallelas diametro, A2, eatamẽ,
in quibus eductæ diuidunt eas parallelas, quæ viciſſim abſcindunt de
ipſis, AL, AF, verſus, A, eandem partem, quam ab ipſis, QL, XF, ab-
ſcindunt eductę, verſus tamen puncta, L, F, vt ex. g. notabimus pun-
ctum, γ, in quo educta, AP, abſcindit {4/5}. ipſius, QL, verſus, L,