Mathesis enucleata, or, The elements of the mathematicks by J. Christ. Sturmius ; made English by J.R. and R.S.S.

CONSECTARYS.

I. HEnce yov have first of all the reason of the name of the Ellipse, which Apollonius gave to this section; viz. because the square of the semiordinate IK is defective of, or less than the rectangle of the Latus Rectum and the abscis∣sa.

II. Since therefore the Latus Rectum here also as well as in the parabola and hyperbola, is found by making as b to c so od to 〈 math 〉〈 math 〉 (i. e. as BM parallel to the section is to the inter∣cept. diam. AM so the Latus Primarium EP to a fourth EL) now if any one had rather express this Latus Rectum after A∣pollonius's way, he will easily see that the quantity above found being multiplyed both Numerator and Denominator by b, that there will come out an equivalent one 〈 math 〉〈 math 〉, which instead of the former proportion will give this other,

as

• bb− to cd− so ob to a fourth;
• BM−▭AMC—Latus Transvers. to a fourth;

which is the same with that we have also found in the hyper∣bola, and which also Apollonius has Prop. 13. Lib. 1.

III. This Latus Rectum may also be had geometrically, if you find, 1. in the hyperbola a third proportional FH to the abscissa EI (Fig. 121.) and semiordinate IK (= EF.) 2. But EL a fourth proportional to DI (the difference of the Latus Transversum and the abscissa) and the found FH, or IS equal to it, and the Latus Transversum DE, is the Latus Rectum sought.