Syntaxis mathematica, or, A construction of the harder problemes of geometry with so much of the conicks as is therefore requisite and other more ordinary and usefull propositions inter-mixed, and tables to several purposes / by Tho. Gibson.

Example.

Let it be

• b=6
• c=3
• d=10

Then	22 dbb = 7920
And	11 dcc = .990
In all	8910

Divide 8910 by 42 the quotient is 212 1/7, which is equall to aaa the content in inches, which was required. The very same number will come forth if one work by the former way, put∣ting circumference to Diameter, as 22 to 7. But although this should be exactly true in one Ves∣sel (which cannot be proved because of the irre∣gularity of the Vessel) it would not be so in others, because of the irregularity (or diversity) of this irregularity.

In Mr. Spidals Extractions there are many Propositions of worth, and all undemonstrated, I will therefore in this place bestow a Demon∣stration on one of the hardest of them, which is this.

Let it be required to divide any Triangle, as

cng from a point without the Triangle as q, into two parts, of which one part shall have any pro∣portion to the whole, given between two right lines, as here the lines cd and cg.

[illustration] mathematical diagram

By the point q draw qa parallel to the nee∣rer side cn, cutting gc, produced, in a. Make aq′ cn″ ac′ cf″, And ac′ bc″ cf′″.

And part cf into two equall parts in the point h, and draw the Diagonall bh, And make he=bh. Lastly, draw the line qe.

Then I say the Triangle cng is divided by the line qe into two parts cme and mnge so, that as cme is to the whole cng, so is cd to cg.