Harriot, Thomas - Mss. 6784

589295

[Commentary:

There is a reference on this page to Proposition II.4 from Conicorum libri quattuor (Apollonius . ]

Alhazen. pag.

Ducere rectam (

a d

) a puncto (

a

)
ut (

e d

) sit æqualis data (

h z

[Translation: Draw a line (

a d

) from the point (

a

) so that (

e d

) is equal to a given (

h z

Ap: 4,2i. fiat per punctum

t

h x z

hyperbola.

t p

. Continuetur

t x

o

et fiat

x o = x t

.
fiat per punctum

o

n x k

hyperbola contraposita

o u

Tum a puncto

t

intelligatur duci

t r

quæ sit minima omnium quæ duci
possunt ad sectionem

r o c u

.
Si

t r

esset sit æqualis diametro

b g

t

fiat centrum et periferia transeat
per

r

, non secabit sectionem sed
tanget in puncto

r

.
Seu cum

b g

sit

> t r

. centro

t

intevallo

b g

describatur periferia

c γ

quæ secabit
oppositum sectionem in duabus punctis

c

\ g a m m e

.
Agantur

t c

t γ

: utræque æqualis

b g

[Translation: Apollonius II.4. Through the point

t

and

h x z

make a hyperbola

t p

.
Continue

t x

o

and make

x 0 = x t

.
Through the point

o

and

n x k

make the opposite hyperbola.
Then from the point

t

there is understood to be ocnstructed

t r

, which is the minimum of all that can be constructed to the segment

r o c u

.
If

t r

is equal to the diameter

b g

and

t

is the centre, and the circumference passes through

r

, it will not cut the segment but touch at the point

r

.
Or when

b g > t r

, with centre

t

and distance

b g

, draw a circumference

c γ

which will cut the opposite segment at the points

c

adn

γ

.
Construct

t c

and

t γ

: both are equal to

b g

t c

, secabit

z n

q

. et

h l

f

.
[…]
Dico quod:

e d = h z

[Translation:

t c

will cut

z n

q

and

h l

f

.

I say that

e d = h z

(per construct.
[Translation: (by the construction

521 (261)	522 (261v)
523 (262)	524 (262v)
525 (263)	526 (263v)
527 (264)	528 (264v)
529 (265)	530 (265v)

List of thumbnails

Text layer

Text normalization

Search