Elements of Plane and Spherical Trigonometry: With Practical ApplicationsR. S. Davis, 1861 - 490 páginas |
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Página 17
... manner it may be shown that the angle CEB is equal to its opposite angle , A ED . 50. Cor . 1. The four angles formed by two straight lines intersecting each other , are together equal to four right angles . 51. Cor . 2. All the ...
... manner it may be shown that the angle CEB is equal to its opposite angle , A ED . 50. Cor . 1. The four angles formed by two straight lines intersecting each other , are together equal to four right angles . 51. Cor . 2. All the ...
Página 19
... manner , since the angle C is equal to the angle F , the line CA will take the direction FD , and the point A will be found some- where in the line F D. Hence the point A , falling at the same time in both of the straight lines ED and ...
... manner , since the angle C is equal to the angle F , the line CA will take the direction FD , and the point A will be found some- where in the line F D. Hence the point A , falling at the same time in both of the straight lines ED and ...
Página 21
... manner it may be proved that the side AC is less than the sum of A B and B C , and the side BC less than the sum of B A and A C. 63. Cor . Since the side AB is less than the sum of A C and CB , if we take away from each of these two ...
... manner it may be proved that the side AC is less than the sum of A B and B C , and the side BC less than the sum of B A and A C. 63. Cor . Since the side AB is less than the sum of A C and CB , if we take away from each of these two ...
Página 25
... manner it may be shown that A D is equal to DF . Therefore A C , the half of the line ACF , is shorter than AD , the half of the line ADF ; hence the oblique line which meets the given line the greater distance from the perpendicular ...
... manner it may be shown that A D is equal to DF . Therefore A C , the half of the line ACF , is shorter than AD , the half of the line ADF ; hence the oblique line which meets the given line the greater distance from the perpendicular ...
Página 29
... manner , it may be shown that the angle B is equal to E , and the angle C to F ; hence the two triangles must be equal . 81. Scholium . In two triangles equal to each other , the equal angles are opposite the equal sides ; thus the ...
... manner , it may be shown that the angle B is equal to E , and the angle C to F ; hence the two triangles must be equal . 81. Scholium . In two triangles equal to each other , the equal angles are opposite the equal sides ; thus the ...
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Términos y frases comunes
A B C ABCD adjacent angles altitude angles ACD angles equal base bisect centre chord circle circumference cone convex surface cosec cosine Cotang diagonal diameter distance divided drawn equal angles equal Prop equiangular equilateral equivalent exterior angle feet four right angles frustum gles greater half the sum homologous homologous sides hypothenuse inches included angle inscribed less Let ABC line A B logarithm mean proportional multiplied parallelogram parallelopipedon perimeter perpendicular polyedron prism PROPOSITION pyramid quadrilateral radii radius ratio rectangle regular polygon right angles Prop right-angled triangle Scholium secant secant line segment side A B side BC similar slant height solidity solve the triangle sphere spherical triangle Tang tangent THEOREM triangle ABC trigonometric functions vertex
Pasajes populares
Página 17 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Página 57 - If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent.
Página 155 - The convex surface of the cylinder is equal to the circumference of its base multiplied by its altitude (Prop.
Página 28 - If any number of quantities are proportional, any antecedent is to its consequent as the sum of all the antecedents is to the sum of all the consequents. Let a : b = c : d = e :f Now ab = ab (1) and by Theorem I.
Página 118 - The radius of a sphere is a straight line, drawn from the centre to any point of the...
Página 98 - If a straight line is perpendicular to each of two straight lines at their point of intersection, it is perpendicular to the plane of those lines.
Página 144 - The convex surface of this prism is equal to the perimeter of its base multiplied by its altitude, AG (Prop.
Página 176 - Find the area of the sector having' the same arc with the segment, and also the area of the triangle formed by the chord of the segment and the radii of the sector. Then...
Página 14 - Straight lines which are parallel to the same line are parallel to each other. Let the straight lines AB, CD be each parallel to the line EF ; then are they parallel to each other.
Página 95 - STRAIGHT line is perpendicular to a plane, when it is perpendicular to every straight line which it meets in that plane.