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
NXad puncta X; _ſumma rectarum_ NX(in radiis) æquatur ſpatio
{AFZK/Rad}; & _ſummarectarum_ NX (in parallelis ad AS) æquatur _ſpatio_
{PLQO/3 Rad. }.

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.

Note to user

Dear user,

In response to current developments in the web technology used by the Goobi viewer, the software no longer supports your browser.

Please use one of the following browsers to display this page correctly.

Thank you.

powered by Goobi viewer