And from a point unto a point is this justly demanded to be done, not unto points; For neither doe all points fall in a right line: But many doe fall out to be in a crooked line. And in a Spheare, a Cone & Cylinder, a Ruler may be applyed, but it must be a sphearicall, Conicall, or Cylindraceall. But by the example of a right line doth Vitellio, 2 p j. demaund that betweene two lines a surface may be extended: And so may it seeme in the Elements, of many figures both plaine and solids, by Euclide to be demanded; That a figure may be described, at the 7. and 8. e ij. Item that a figure may be made vp, at the 8. 14. 16. 23. 28. p. vj. which are of Plaines. Item at the 25. 31. 33. 34. 36. 49. p. xj. which are of Solids. Yet notwithstanding a plaine surface, and a plaine body doe measure their rectitude by a right line, so that jus postulandi, this right of begging to have a thing granted may seeme primarily to bee in a right plaine line.
Now the Continuation of a right line is nothing else, but the drawing out farther of a line now drawne, and that from a point unto a point, as we may continue the right line ae. unto i. wherefore the first and second Petitions of Euclide do agree in one.
And
7. To set at a point assigned a Right line equall to another right line given: And from a greater, to cut off a part equall to a lesser. 2. and 3. p j.
As let the Right line given be ae. And to i. a point assigned, grant that io. equall to the same ae. may bee set. Item, in the second example, let ae. bee greater then io. And let there be cut off from the same ae. by applying of a rular made equall to io. the lesser, portion au. as here. For if any man shall thinke that this ought only to be don in the minde, hee also, as it were, beares a ruler in his minde, that he may doe it by the helpe of the ruler. Neither is the fabricke in deede, or making of one right equal to another: And the cutting off from greater Right line, a portion equall to a lesser, any whit harder, then it was, having a point and a distance given, to describe a circle: Then having a Triangle, Parallelogramme, and semicircle given, to describe or make a Cone, Cylinder, and spheare, all which notwithstanding Euclide did account as principles.
Therefore,
8. One right line, or two cutting one another, are in the same plaine, out of the 1. and 2. p xj.