declared by shorte examples. (continued 2)

The lxxvii. Theoreme.

If a pointe be assigned without a circle, and from that pointe .ij. right lynes be drawen to the circle, so that the one doe crosse the circle, and the other dooe ende at the circumference, and that the longsquare of the line which crosseth [m.i.v]

Example.

In as muche as this Theoreme is nothyng els but the sentence of the last Theoreme before conuerted, therfore it shall not be nedefull to vse any other example then the same, for as in that other Theoreme because the one line is a touche lyne, therfore it maketh a square iust equal with the longsquare made of that whole line, whiche crosseth the circle, and his portion liyng without the same circle. So saith this Theoreme: that if the iust square of the line that endeth on the circumference, be equall to that longsquare whiche is made as for his longer sides of the whole line, which commeth from the pointt assigned, and crosseth the circle, and for his other shorter sides is made of the portion of the same line, liyng betwene the circumference of the circle and the pointe assigned, then is that line whiche endeth on the circumference a right touche line, that is to saie, yf the full square of the right line A.B, be equall to the longsquare made of the whole line A.C, as one of his lines, and of his portion A.D, as his other line, then must it nedes be, that the lyne A.B, is a right touche lyne vnto the circle D.B.C. And thus for this tyme I make an ende of the Theoremes.

FINIS,

[m.ii.]

IMPRINTED at London in Poules churcheyarde, at the signe of the Bra- senserpent, by Reynold Wolfe.

Cum priuilegio ad imprimen- dum solum.

ANNO DOMINI .M.D.L.I.

[m.ii.

v

]

Title page:

The pathway to KNOWLEDG, CONTAI- NING THE FIRST PRIN- ciples of Geometrie, as they may moste aptly be applied vn- to practice, bothe for vse of instrumentes Geome- tricall, and astrono- micall and also for proiection of plattes in euerye kinde, and therfore much ne- cessary for all sortes of men.

Dedication:

TO THE MOST NO- ble and puissaunt prince Edwarde the sixte by the grace of God, of En- gland Fraunce and Ireland kynge, de- fendour of the faithe, and of the Churche of England and Ire- lande in earth the su- preme head.

Title page of Second Book:

THE SECOND BOOKE OF THE PRINCIPLES of Geometry, containing certaine Theoremes, whiche may be cal- led Approued truthes. And be as it were the moste certaine groundes, wheron the practike cõclusions of Geometry ar founded.

[Leaf]

Whervnto are annexed certaine declarations by examples, for the right vnderstanding of the same, to the ende that the simple reader might not iustly cõplain of hardnes or obscuritee, and for the same cause ar the demonstra- tions and iust profes omitted, vntill a more conueni- ent time.

1551.

“Theorems of Geometry”:

The Theoremes of Geometry, before WHICHE ARE SET FORTHE certaine grauntable requestes which serue for demonstrations Mathematicall.