Harriot, Thomas - Mss. 6787

754378

1.) De
[Translation: 1) On the ]

Datis tribus punctis
quorum unum ponitur in
centro de et caetera
duo in parabola:
Invenire
[Translation: Given three points of which one is supposed in the centre

d e

and the other two on the parabola, find the parabola.

Sint tria puncta,

a

b

c

a

, centroidis.

b

c

, in
[Translation: Let there be three points

a

b

c

;

a

the focus,

b

and

c

on the parabola.

fiat circulus cuius
diameter

a b

et fit

a h b

.
fiat alter circulus cuius semidiameter

a b

et
fit

b d

.
punctum

b

est in infini-
tis parabolis et locus
omnium verticum est
in spirali quaedam propria

a

g

b

quae fit ex medijs
punctis inter periferias
circulorum
[Translation: Make the circle whose diameter is

a b

and construct

a h b

.
Make another circle whose semidiameter is

a b

and construct

b d

.
The point

b

is on an infinite parabola and the locus of all vertices is on the spiral through

a

g

b

, which is constructed from the midpoints between the circumferences of the described circles.

Deinde fiat circulus
cuius diameter

a c

et fit

a k c

.
Fiat alter circulus cuius
semidiameter

a c

et fit

c f

[Translation: Then make the circle whose diameter is

a c

and construct

a k c

.
Make another circle whose semidiameter is

a c

and construct

c f

punctum

c

est in infinitis
parabolis, et locus omnium
vertica, est similis
altera spiralis

a g c

.
quae fit ex medijs punctus
inter periferias ultimo

[Translation: The point

c

is on an infinite parabola, and the locus of all vertices is another spiral

a g c

, which is constructed from the midpoints between the circumferences last described.

Et ubi secant duae spralis
ut in puncto

g

, ibi est
vertex parabola in qua sint
duo puncta

b

c

[Translation: And where the two spirals cut, as in point

g

, there is the vertex of the parabola in which lie the two points

b

and

c

Iugantur puncta

a

g

.
linea

a g

producatur,
et secabit periferias in

d

f

. et reliqus peri-
ferias in

k

h

, secabat.
[Translation: Let the points

a

and

g

be joined, and the line

a g

extended cut the circumferences in

d

and

f

. And it will cut the other circumference in

k

and

h

. *

* Agantur rectam

b h

c k

, quae faciunt
angulos rectos cum

a g

. Et sint
lineae ordinatim applicatam.
Si agatur recta

d b

, tanget parabolam
in puncto

b

.
Si agatur recta

f e

, tanget parabolam
in puncto

c

.
Nam

g

est medium punctum inter

h

d

.
et inter

k

f

[Translation: * Take the lines

b h

c k

, which make right angles with

a g

. And these lines are ordinates.
If the line

d b

is taken, it touches the parabola at the point

b

.
If the line

f c

is taken, it touches the parabola at the point

c

.
For

g

is the midpoint between

h

and

d

and between

k

and

f

Constructio geometrica
fit per poristica
[Translation: The geometric construction is by the following ]

691 (346v)	692 (347)
693 (347v)	694 (348)
695 (348v)	696 (349)
697 (349v)	698 (350)
699 (350v)	700 (351)

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