Elements of Geometry, and Plane and Spherical Trigonometry: With Numerous Practical Problems |
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Page 11
... perpendicular to each other . 16. An Acute Angle is less than a right angle . 17. An Obtuse Angle is greater than a right angle . Obtuse and acute angles are also called oblique angles ; and lines which are neither parallel nor perpen ...
... perpendicular to each other . 16. An Acute Angle is less than a right angle . 17. An Obtuse Angle is greater than a right angle . Obtuse and acute angles are also called oblique angles ; and lines which are neither parallel nor perpen ...
Page 14
... perpendicular distance between the base and a side or angle opposite the base . 45. Equal Magnitudes are those which are not only equal in all their parts , but which also , when applied the one to the other , will coincide throughout ...
... perpendicular distance between the base and a side or angle opposite the base . 45. Equal Magnitudes are those which are not only equal in all their parts , but which also , when applied the one to the other , will coincide throughout ...
Page 18
... Perpendicular is expressed by · The difference of two quantities , when it is not known which is the greater , is ex- pressed by the symbol • Thus , the difference between A and B is written AN B .. BOOK I. OF STRAIGHT LINES , ANGLES ...
... Perpendicular is expressed by · The difference of two quantities , when it is not known which is the greater , is ex- pressed by the symbol • Thus , the difference between A and B is written AN B .. BOOK I. OF STRAIGHT LINES , ANGLES ...
Page 31
... perpendicular to the sides of a second angle , these two angles will be either equal or supplementary . Let BAD be the first angle , and from any point within it , as C , draw CB and CD , at right angles , the first to AB , and the ...
... perpendicular to the sides of a second angle , these two angles will be either equal or supplementary . Let BAD be the first angle , and from any point within it , as C , draw CB and CD , at right angles , the first to AB , and the ...
Page 34
... perpendicular to the base . SCHOLIUM 1. — If in the perpendicular DC , any other point than C be taken , and lines be drawn to the extremities A and B , such lines will be equal , as is evident from Th . 16 ; hence , we may announce ...
... perpendicular to the base . SCHOLIUM 1. — If in the perpendicular DC , any other point than C be taken , and lines be drawn to the extremities A and B , such lines will be equal , as is evident from Th . 16 ; hence , we may announce ...
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Common terms and phrases
ABCD altitude angle opposite axis bisected chord circle circumference circumscribed common cone convex surface cos.a cos.c Cosine Cotang diagonal diameter dicular difference distance divided draw equal angles equation equiangular equivalent find the angles four magnitudes frustum given line greater half Hence the theorem homologous hypotenuse included angle inscribed intersect isosceles less Let ABC logarithm measured multiplied N.sine number of sides opposite angles parallelogram parallelopipedon pendicular perpen perpendicular plane ST polyedron PROB PROBLEM produced Prop proportion PROPOSITION prove pyramid quadrantal radii radius rectangle regular polygon right angles right-angled spherical triangle right-angled triangle SCHOLIUM secant segment similar sin.a sin.b sin.c sine solid angles sphere SPHERICAL TRIGONOMETRY square straight line Tang tangent three angles three sides triangle ABC triangular prisms Trigonometry vertex vertical angle volume
Popular passages
Page 322 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
Page 30 - Therefore all the interior angles of the figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Page 123 - In a given circle to inscribe a triangle equiangular to a given triangle. Let ABC be the given circle, and DEF the given triangle ; it is required to inscribe in the circle ABC a triangle equiangular to the triangle DEF.
Page 58 - 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 of the line between the points of section, is equal to the square of half the line.
Page 29 - If one side of a triangle is produced, the exterior angle is equal to the sum of the two interior and opposite, angles; and the three interior angles of every triangle are equal to two right angles.
Page 41 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Page 96 - The angle in a semicircle is a right angle ; the angle in a segment greater than a semicircle is less than a right angle ; and the angle in a segment less than a semicircle is greater than a right angle.
Page 65 - In a series of equal ratios, any antecedent is to its consequent, as the sum of all the antecedents is to the sum of all the consequents. Let a: 6 = c: d = e :/. Then, by Art.
Page 77 - FGL ; (vi. 6.) and therefore similar to it ; (vi. 4.) wherefore the angle ABE is equal to the angle FGL: and, because the polygons are similar, the whole angle ABC is equal to the whole angle FGH ; (vi.
Page 113 - From a given point, to draw a line parallel to a given line. Let A be the given point, and BC the given line.