The geometry, by T. S. Davies. Conic sections, by Stephen FenwickJ. Weale, 1853 - Mathematics |
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Page 10
... perpendicular to a given straight line of an unlimited length , from a given point without it . Let AB be the given straight line , which may be produced to any length both ways , and let C be a point without it . It is required to draw ...
... perpendicular to a given straight line of an unlimited length , from a given point without it . Let AB be the given straight line , which may be produced to any length both ways , and let C be a point without it . It is required to draw ...
Page 31
... perpendicular from A upon BC ; ( c ) The lines BK , CF are respectively perpendicular to AE , AD ; ( d ) The squares described on the sides BA , AC about the right angle are equal to the rectangles under the hypothenuse and the segments ...
... perpendicular from A upon BC ; ( c ) The lines BK , CF are respectively perpendicular to AE , AD ; ( d ) The squares described on the sides BA , AC about the right angle are equal to the rectangles under the hypothenuse and the segments ...
Page 32
... perpendicular from the right angle upon the hypothenuse , an angle equal to the difference of the acute angles of ... perpendicular can be drawn from a given point to a given straight line , whether the point be in the line or without it ...
... perpendicular from the right angle upon the hypothenuse , an angle equal to the difference of the acute angles of ... perpendicular can be drawn from a given point to a given straight line , whether the point be in the line or without it ...
Page 41
... perpendicular falls , and the straight line intercepted without the triangle , between the perpendicular and the obtuse angle . Let ABC be an obtuse - angled triangle , having the obtuse angle ACB , and from the point A let AD be drawn ...
... perpendicular falls , and the straight line intercepted without the triangle , between the perpendicular and the obtuse angle . Let ABC be an obtuse - angled triangle , having the obtuse angle ACB , and from the point A let AD be drawn ...
Page 42
... perpendicular ( 12. 1. ) AD from the opposite angle : the square of AC , opposite to the angle B , is less than the ... perpendicular to BC ; then is BC the straight line between the perpendicular and the acute angle at B : and it is ...
... perpendicular ( 12. 1. ) AD from the opposite angle : the square of AC , opposite to the angle B , is less than the ... perpendicular to BC ; then is BC the straight line between the perpendicular and the acute angle at B : and it is ...
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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.