Harriot, Thomas - Mss. 6784

18191

[Commentary:

The problem pursued in this and many other folios in Add MS 6784 is 'the cutting-off of an area', as set out in Pappus, Mathematicae collectiones (Pappus , Book 7. For a statement of the problem see Add MS 6784 f. . ]

1. problematis de spatij resectione 4a demonstratione et
[Translation: Problems of cutting off of an area, demonstration and most ]

Quatuor possunt esse
resectiones ab uno
puncto dato et duabus
solummodo lineis datis;
secundum quantitatem
spatij dati
aliquando tres:
semper
[Translation: There are four possible sections from one given point and just two given lines, according to the size of the given area; sometimes three, always two.

Exegesis.
producetur

A C

usque ad

L

et fiat

C L

æqualis

D E

cui etiam sit æqualis
sit

A M

. Around

M

intervallo

A L

agatur periferia

F Z O

.
Ab

E

puncto, per

O

F

Ducatur rectæ

E F

E W

.
Dico
[Translation: Exegesis.
Let

A C

be extended as far as

L

and make

C L

equal to

D E

to which

A M

is also equal. Around

M

with radius

A L

there is constructed the circumference

F Z O

. From the point

E

, through

O

and

F

there are drawn the lines

E F

and

E W

.
I say ]

Poristice et inde
synthesis manifesta The poristic, and hence the synthesis, is obvious.

D E

sit æqualis

D C

tum:

C O = C G

Nam

C L E D

erit quadratum
et punctum

E

[???]
[???].
Sit

D E

sit maior

D C

. tum

F C

est maximum secta [???]
et

C G

[Translation: If

D E

is equal to

D C

, then

C O = C G

.
For

C L E D

will be a square, and the point

E

[???].
If

D E

is greater than

D C

, then

F C

is the maximum segment and

C G

the minimum.

121 (61)	122 (61v)
123 (62)	124 (62v)
125 (63)	126 (63v)
127 (64)	128 (64v)
129 (65)	130 (65v)

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