The geometry, by T. S. Davies. Conic sections, by Stephen FenwickJ. Weale, 1853 - Mathematics |
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Page 20
... drawing straight lines from a point F within the figure to each of its angles . And , by the preceding proposition , all the angles of these triangles are A D C equal to twice as many right angles as there are 20 EUCLID'S ELEMENTS .
... drawing straight lines from a point F within the figure to each of its angles . And , by the preceding proposition , all the angles of these triangles are A D C equal to twice as many right angles as there are 20 EUCLID'S ELEMENTS .
Page 37
... preceding propositions ; And because AG is equal ( 43. 1. ) to GE , add to each of them CK ; the whole AK is therefore equal to the whole CE ; therefore AK , CE are double of AK : A C B But AK , CE are the gnomon AKF , together with the ...
... preceding propositions ; And because AG is equal ( 43. 1. ) to GE , add to each of them CK ; the whole AK is therefore equal to the whole CE ; therefore AK , CE are double of AK : A C B But AK , CE are the gnomon AKF , together with the ...
Page 56
... preceding , BC is double of BH , and FG double of FK , and the squares of EH , HB are equal to the squares EK , KF , of which the square of EH is less than the square of EK , because EH is less than EK ; therefore the square of BH is ...
... preceding , BC is double of BH , and FG double of FK , and the squares of EH , HB are equal to the squares EK , KF , of which the square of EH is less than the square of EK , because EH is less than EK ; therefore the square of BH is ...
Page 71
... preceding exercise is virtually identical with this . 11. Except one pair of opposite angles together be equal to the other pair together in a quadrilateral , a circle cannot be described about the quadrilateral ; but if that condition ...
... preceding exercise is virtually identical with this . 11. Except one pair of opposite angles together be equal to the other pair together in a quadrilateral , a circle cannot be described about the quadrilateral ; but if that condition ...
Page 82
... preceding proposition , that the angles . CBA , BAE , AED are bisected by the straight lines FB , FA , FE : And because the angle BCD is equal to the angle CDE , and that FCD is the half of the E angle BCD , and CDF the half of CDE ...
... preceding proposition , that the angles . CBA , BAE , AED are bisected by the straight lines FB , FA , FE : And because the angle BCD is equal to the angle CDE , and that FCD is the half of the E angle BCD , and CDF the half of CDE ...
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Common terms and phrases
ABC is equal ABCD angle ABC angle BAC axis bisected centre circle ABC circumference coincide cone conic section construction coordinate planes curve described Descriptive Geometry dicular dihedral angles directrix distance draw edges ellipse equal angles equiangular equimultiples given line given point given straight line greater hence inclination intersection join less Let ABC Let the plane line BC lines drawn magnitudes meet multiple opposite orthograph parabola parallel planes parallelogram parallelopiped perpen perpendicular plane MN plane of projection plane parallel plane PQ prisms profile angles profile plane projecting plane projector Prop Q. E. D. PROPOSITION ratio rectangle rectangle contained rectilineal figure remaining angle respectively right angles SCHOLIUM segment sides six right sphere spherical spherical angle tangent THEOR trace triangle ABC trihedral vertex vertical plane Whence Wherefore
Popular passages
Page 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.
Page 35 - If a straight line be divided into two equal parts, and also into two unequal parts ; the rectangle contained by the unequal parts, together with the square on the line between the points of section, is equal to the square on half the line.
Page 4 - AB; but things which are equal to the same are equal to one another...
Page 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.
Page 8 - If two triangles have two sides of the one equal to two sides of the...
Page 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...
Page 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.
Page 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.
Page 4 - Magnitudes which coincide with one another, that is, which exactly fill the same space, are equal to one another.
Page 116 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.