138AD LECTOREM.
tæ;
neque quantum ſcio ab ullo alio tractata eſt
hæc materia, etiamſi geometriæ ſpeculativæ non ſo-
lum utiliſſima ſit, ſed etiam maxime admirabilis;
in ipſo enim limine admiranda occurrunt theorema-
ta;
e.
g.
Si fuerit progreſſio geometrica cujus unus
terminus fuerit propoſitæ quantitati commenſurabi-
lis longitudine vel poteſtate quacunque, &
alius
quilibet, binomium, trinomium, &
c.
quodcunque,
impoſsibile eſt duos totius progreſſionis terminos in
infinitum continuatæ eſſe inter ſe commenſurabiles
longitudine vel poteſtate quacunque:
alia multa
poſſem afferre, ſed pro commodiore fortaſſis tempo-
re hæc reſervo, ſatis exiſtimans pro præſenti hæc
analyticè demonſtraſſe;
etſi enim analyſis aſſenſum
adeo violenter non cogat ac geometria, nunquam ta-
men reſpuit nec reſpuere poteſt geometria, quodpro-
bavit ſemel analyſis geometrica.
Ex hac inventione
deduco quoque novam ſectionem angularium &
lo-
gorithmorum doctrinam, facilem quidem, in praxi
expeditiſsimam &
geometrica demonſtratione muni-
tam;
hactenus enim logorithmorum conſtructio pro-
lixiſſima, conjectura potius quam ſcientia videba-
tur, &
diviſio anguli in partes æquales ultra quin-
que numero primo numeratas in praxim vix ad-
mitti poterat.
hæc omnia ſumma (qua poſſum) bre-
vitate &
perſpicuitate demonſtro;
neque ſcrupulo-
ſus ſum in citationibus, utpote peregrinus, &
li-
bris ad tale opus deſtitutus, te enim ſuppono in
geometricis non mediocriter verſatum, alioquin
[41.] Theor. XII. Prop. XV.
[42.] Theor. XIII. Prop. XVI.
[43.] Theorema XIV. Propos. XVII.
[44.] Theor. XV. Propos. XVIII.
[45.] Theor. XVI. Propos. XIX.
[46.] Problema IV. Propos. XX.
[47.] Christiani Hugenii C. F. ILLVSTRIVM QVORVNDAM PROBLEMATVM CONSTRVCTIONES. Probl. I. Datam ſphæram plano ſecare, ut portiones inter ſe rationem habeant datam.
[48.] LEMMA.
[49.] Probl. II. Cubum invenire dati cubi duplum.
[50.] Probl. III. Datis duabus rectis duas medias propor-tionales invenire.
[51.] ALITER.
[52.] ALITER.
[53.] Probl. IV.
[54.] Probl. V.
[55.] Probl. VI.
[56.] Probl. VII.
[57.] Utrumque præcedentium Aliter.
[58.] Probl. VIII. In Conchoide linea invenire confinia flexus contrarii.
[59.] FINIS.
[60.] DE CIRCULI ET HYPERBOLÆ QUADRATURA CONTROVERSIA.
[61.] VERA CIRCULI ET HYPERBOLÆ QUADRATURA AUTHORE JACOBO GREGORIO. LECTORI GEOMETRÆ SALUTEM.
[62.] DEFINITIONES.
[63.] PETITIONES.
[64.] VERA CIRCULI ET HYPERBOLÆ QUADRATURA.
[65.] PROP. I. THEOREMA. Dico trapezium B A P I eſſe medium propor-tionale inter trapezium B A P F, & triangulum B A P.
[66.] PROP. II. THEOREMA. Dico trapezia A B F P, A B I P ſimul, eſſe ad du-
plum trapezii A B I P, ſicut trapezium A B F P
ad polygonum A B D L P.
[67.] PROP. III. THEOREMA. Dico triangulum B A P, & trapezium A B I P ſimul,
eſſe ad trapezium A B I P, ut duplum trapezii
A B I P ad polygonum A B D L P.
[68.] PROP. IV. THEOREMA. Dico polygonum A B E I O P eſſe medium pro-
portionale inter polygonum A B D L P
& trapezium A B I P.
[69.] PROP. V. THEOREMA.
[70.] SCHOLIUM.