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ABC is equal ABCD adjacent angles angle ABC angle BAC axis bisected centre circle ABC circumference coincide cone conic section construction coordinate planes describe Descriptive Geometry diameter dicular dihedral angles draw edges eidograph ellipse equal angles equiangular equimultiples exterior angle given line given point given straight line greater hence hyperbola inclination intersection join less Let ABC Let the plane line BC line drawn magnitudes meet multiple orthograph parabola parallel planes parallelogram parallelopiped perpen perpendicular perspective plane MN plane of projection plane parallel plane PQ prism profile angles profile plane projecting plane projector Prop q. e. d. PROPOSITION ratio rectangle contained rectilineal figure remaining angle right angles Scholium segment sides sphere spherical angle tangent Theor trace triangle ABC trihedral vanishing point vertex vertical plane Whence Wherefore
Side 19 - That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.
Side 4 - AB; but things which are equal to the same are equal to one another...
Side 128 - EQUIANGULAR parallelograms have to one another the ratio which is compounded of the ratios of their sides.* Let AC, CF be equiangular parallelograms, having the angle BCD equal to the angle ECG : the ratio of the parallelogram AC to the parallelogram CF, is the same with the ratio which is compounded of the ratios of their sides. Let BG, CG, be placed in a straight line ; therefore DC and CE are also in a straight line (14.
Side 8 - If two triangles have two sides of the one equal to two sides of the...
Side 36 - If a straight line be bisected and produced to any point, the rectangle contained by the whole line thus produced and the part of it produced...
Side 21 - BCD, and the other angles to the other angles, (4. 1.) each to each, to which the equal sides are opposite : therefore the angle ACB is equal to the angle CBD ; and because the straight line BC meets the two straight lines AC, BD, and makes the alternate angles ACB, CBD equal to one another, AC is parallel (27. 1 .) to DB ; and it was shown to be equal to it. Therefore straight lines, &c.
Side 65 - If a straight line touch a circle, and from the point of contact a straight line be drawn cutting the circle, the angles which this line makes with the line touching the circle shall be equal to the angles which are in the alternate segments of the circle.
Side 4 - Magnitudes which coincide with one another, that is, which exactly fill the same space, are equal to one another.