Barrow, Isaac, Lectiones opticae & geometricae : in quibus phaenomenon opticorum genuinae rationes investigantur, ac exponuntur: et generalia curvarum linearum symptomata declarantur

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Quòd NYG ſit una recta patet, quoniam eſt YB. BN : : GD.
DY (ex conſtructione nimirum) porrò per Y tranſeat alia quæcunque
recta
LYM;
& NH ad GN, MH ad PF perpendiculares concur-
rant
in H.
item HA ad NG parallela ducatur; & GS ad PF;
denuóque
connectatur GH.
Jam patet triangula GDY, YBN,
HMN
, HMR ſimilia fore;
quódque proptereà eſt MN. MR : :
MN
q.
MHq : : DGq. YDq. item (ob BN, DG, YD {. ./. .})
eſt
BN.
YD : : DGq. YDq. hoc eſt YN. YG (vel MN. GS)
:
: DGq. YDq. ergò eſt MN. MR : : MN. GS. adeóque MR
= GS.
itaque major eſt GS ipsâ MT; abeóque rectæ GH, LM
protractæ
concurrent;
puta ad Z. ergò LM. GH : : LZ. GZ.
verùm
propter angulum LGH recto P majorem, eſt LZ &
gt; GZ.
quare
LM &
gt; GH. aſt ob angulum rectum GNH eſt GH & gt; GN.
quare
magìs eſt LM &
gt; GN. eodémque modo quævis per Y ducta
major
oſtendetur ipsâ GN :
Q. E. D.
X. Hinc etiam ſi GN ſit in ratione YB ad YN quarta proportio-
nalis
;
erit GN minima. nam indè conſequetur fore YB, BN, GD,
YD
{.
./. .}. Etenim erit YNq. YBq : : GN. YN. & dividendo
BNq
.
YBq : : GY. YN : : DY . BN. ac indè YBq x DY =
BNcub
;
velDY = {BN cub/YBq}. itáque DY eſt quarta proportionalis in ra-
tione
YB ad BN.
XI. Subnotari poteſt autem, quòd minimæ GN propiores

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