# Full text: Barrow, Isaac: Lectiones Opticæ & Geometricæ

_utin circumf._ AMB ſumpto utcunque puncto M, & per hoc trajectâ
rectâ BMZ, ductâque rectâ MFZ, quæ curvam AZZ ſecet in Z,
ſit MZ = AS) in recta verò α β ſumatur αμ æqualis arcui AM, & ad αμ applicentur rectæ perpendiculares μ ξ æquales _arcunm_ AMſinu-
_bus verſis_ AF; erit _ſpatium trilineum_ MAZ _ſpatii αμξ duplum._

### 45.1.

Fig. 171.
Fig. 171.

Nam ſumatur _arcus_ MNindeſinitè parvus, & ei æqualis μν; du-
catúrque recta NRad ABparallela, connectatúrque recta CM. Eſt-
que jam AS. AB (2 CM): : (FM. FB: :) AF. FM. & 2 CM. 2 MN: : CM. MN: :) FM. NR. quapropter erit ex æquo AS. 2 MN: : AF. NR; & ideò NR x AS = 2 MN x AF. hoc eſt
NR x MZ = 2 μν x μξ. unde _ſpatium_ MAZ _duplo ſpatio_ α μξ æ-
quatur.

Hinc cum _ſpatii_ αμξ dimenſio vulgò nota ſit, & è ſuprà poſitis
etiam facilè deducatur; habetur _ſpatii ciſſoidalis_ MAZ _dimenſio._ cal-
culum ineat qui volet.

### 45.1.

Fig 172.

Iſta claudet hoc _Conſectariolum:_

XV. Sit _circuli quadrans_ ACB, _circulúmque_ tangant AH, BG; ſintque curvæ KZZ, LEO _byperbolœ_, eædem quæ ſuperiùs. ar- cus verò ſumptus AMin partes diviſus concipiatur indefinitè multas
punctis N; per quæ trajiciantur radii CN; & his occurrant rectæ

### 45.1.

Fig. 173.
7, & 12.

Nam triangulum XMN triangulo SAC ſimile eſt; & inde XM. MN: : AS. CA. & XN. MN: : CS. CA. unde XM =
{MN x AS/CA}; & XN = {MN x CS/CA}. & ità in reliquis; unde liquet
Proſitum, ex 2, & 7 harum.

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