Viviani, Vincenzo, De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei

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[211.] Pag. 131. poſt Prop. 84.
[212.] Pag. 144. ad calcem Prop. 93.
[213.] SCHOLIVM.
[214.] Pag. 147. ad finem Prop. 97.
[215.] FINIS.
[216.] DE MAXIMIS, ET MINIMIS GEOMETRICA DIVINATIO In Qvintvm Conicorvm APOLLONII PERGÆI _IAMDIV DESIDERATVM._ AD SER ENISSIMVM PRINCIPEM LEOPOLDVM AB ETRVRIA. LIBER SECVNDVS. _AVCTORE_ VINCENTIO VIVIANI.
[217.] FLORENTIÆ MDCLIX. Apud Ioſeph Cocchini, Typis Nouis, ſub Signo STELLÆ. _SVPERIORVM PERMISSV._
[218.] SERENISSIMO PRINCIPI LEOPOLODO AB ETRVRIA.
[219.] VINCENTII VIVIANI DE MAXIMIS, ET MINIMIS Geometrica diuinatio in V. conic. Apoll. Pergæi. LIBER SECVNDVS. LEMMA I. PROP. I.
[220.] LEMMA II. PROP. II.
[221.] THEOR. I. PROP. III.
[222.] LEMMA III. PROP. IV.
[223.] THEOR. II. PROP. V.
[224.] THEOR. III. PROP. VI.
[225.] LEMMA IV. PROP. VII.
[226.] THEOR. IV. PROP. VIII.
[227.] THEOR. V. PROP. IX.
[228.] SCHOLIVM.
[229.] THEOR. VI. PROP. X.
[230.] THEOR. VII. PROP. XI.
[231.] THEOR. VIII. PROP. XII.
[232.] THEOR. IX. PROP. XIII.
[233.] THEOR. X. PROP. XIV.
[234.] THEOR. XI. PROP. XV.
[235.] LEMMA V. PROP. XVI.
[236.] COROLL.
[237.] THEOR. XII. PROP. XVII.
[238.] THEOR. XIII. PROP. XVIII.
[239.] THEOR. XIV. PROP. XIX.
[240.] PROBL. I. PROP. XX.
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PROBL. I. PROP. VI.
Dato triangulo, cuius vnuſquiſq; angulorum minor ſit gr. 120.
punctum reperire, à quo ſi ad angulos tres rectę educantur, ipſarum
aggregatum ſit MINIMVM.
ESto triangulum A B C vt ponitur, & inuenire oporteat punctum quale
imperatum eſt.
Super latera B A, B C ad partes baſis A C deſcribantur circuli portio-
nes A D B, C D B capientes angulos grad.
120. ſiue æquales externo cuiuſ-
libet trianguli æquilateri, quarum portionum arcus omnino ſe mutuò 115. App. cabunt intra triangulum A B C, ſitque eorum interſectio punctum D.
Di-
co ipſum eſſe quæſitum.
Nam iunctis D A, D B, D C, erunt an-
267[Figure 267] guli A D B, C D B graduum 120.
vnde reli-
quus A D C, vſque ad quatuor rectorum cõ-
plementum item erit gr.
120. Cum ergo tres
rectę D A, D B, D C ad punctum D coeun-
tes tres æquales angulos efficiant, cumque hi
ſimul ſumpti æquales ſint quatuor rectis, erit
ipſarum D A, D B, D C aggregatum _MINIMA_ quantitas.
Quare 224. App. uentum eſt punctum D, vti quærebatur. Quod faciendum erat.
PROBL. II. PROP. VII.
Datam rectam lineam terminatam ita diuidere, vt ſumpta par-
tium ipſius tertia proportionali, aggregatum extremarum ſit MI-
NIMA quantitas.
ESto data linea A B, quam ſecare oporteat, vt imperatum eſt.
Erigatur ex A ipſi A B perpendicularis, & æqualis A D, iunctaq; D
B ſecetur D E æqualis D A, &
ex E ſuper A B perpendicularis demitta-
tur E C.
Dico punctum C quæſitum ſoluere.
Nam bifariam ſecto angulo A D E per rectam D F ſecante A B in F, &
iuncta F E:
cum ſit latus D A æquale D E, & D F commune, & anguli
A D F, E D F æquales, erunt baſes F A, F E æquales, &
reliquus angulus
F E D reliquo F A D æqualis ſiue rectus:
quare ſi cum centro F interuallo
F A circulus deſcribatur A E G, is tranſibit quoque per E, &
vtramque D.
A, D B continget in A, E.
Iam cum in ſemi-circulo ſit A C ad C E, vt C E ad C G, ſitque C B
æqualis C E (cum etiam A D ſit æqualis A B) erit A C ad C B, vt C B
ad C G.
Vnde aggregatum extremarum poſt ſegmenta A C, C B erit A
G;
quod eſſe _MINIMVM_ ſic demonſtrabitur.

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