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

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[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.
[241.] MONITVM.
[242.] THEOR. XV. PROP. XXI.
[243.] PROBL. II. PROP. XXII.
[244.] PROBL. III. PROP. XXIII.
[245.] MONITVM.
[246.] THEOR. XVI. PROP. XXIV.
[247.] THEOR. XVII. PROP. XXV.
[248.] COROLL.
[249.] THEOR. XIIX. PROP. XXVI.
[250.] COROLL. I.
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22644 NVM ACVMINATVM REGVLARE, vel potius (breuitatis cauſa)
ACVMINATVM, cuius terminus B vocetur VERTEX;
& æquidiſtan-
tes A C, E F, G H, &
c. quæ à B D bifariam diuiduntur, dicantur AP-
PLICAT Æ ad ipſam B D, qnæ vocetur DIAMETER, vel AXIS quan-
do ipſa perpendiculariter ſecet eaſdem applicatas.
A C verò dicatur BA-
SIS ACVMINATI;
& B I, quæ à vertice ſuper baſim ducitur perpen-
dicularis, ACVMINATI ALTITVDO nuncupetur.
II.
PLANA ACVMINATA REGVLARIA PROPORTIONALIA, vel
tantùm ACVMINATA PROPORTIONALIA dicantur illa, quorum
omnes applicatæ à punctis eorum diametros proportionaliter diuidenti-
bus, ſint quoque inter ſe proportionales.
Sint nempe duo Acu-
189[Figure 189] minata Regularia ABC,
E F G, ſuper baſes A C,
E G, qualia in præce-
denti definitione expli-
cauimus, quorum dia-
metri B D, F H propor-
tionaliter ſectæ ſint in
quotcunque punctis I,
M;
L, N, & c. ſiue ſit B I
ad I D, vt F M ad M H,
&
B L ad L D, vt F N
ad N H, &
c. atque m
punctis inter ſectionum
applicatæ ſint O P, QR;
S T, V X, quę ex homo-
logis punctis ſint ad inuicem proportionales, hoc eſt vt A C ad E G, ita
O P ad S T, &
Q R ad V X, & c. huiuſmodi figuræ vocentur PLANA
ACVMINATA REGVLARIA PROPORTIONALIA, veltantùm ACV-
MINATA PROPORTIONALIA.

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