Elements of Geometry, Conic Sections, and Plane TrigonometryHarber & brothers, 1871 - 58 páginas |
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Página 16
... ( Prop . II , Cor . 1 ) ; and since ACE is a straight line , the angle FCE is also a right angle ; therefore ( Prop . I. ) , the angle FCE is equal to the angle FCD , the less to the greater , which L absurd . Therefore , two straight ...
... ( Prop . II , Cor . 1 ) ; and since ACE is a straight line , the angle FCE is also a right angle ; therefore ( Prop . I. ) , the angle FCE is equal to the angle FCD , the less to the greater , which L absurd . Therefore , two straight ...
Página 21
... ( Prop . VIII . ) ; it is , therefore , less than AB . Conversely , if the side AB is greater than the side AC , then will the angle ACB be greater than the angle ABC . For if ACB is not greater than ABC , it must be either equal to it ...
... ( Prop . VIII . ) ; it is , therefore , less than AB . Conversely , if the side AB is greater than the side AC , then will the angle ACB be greater than the angle ABC . For if ACB is not greater than ABC , it must be either equal to it ...
Página 22
... ( Prop . VI . ) , which is contrary to the suppo- sition . Neither is it less , because then the base BC would be less than the base EF ( Prop . XIII . ) , which is also contrary to the supposition ; therefore , the angle BAC is not less ...
... ( Prop . VI . ) , which is contrary to the suppo- sition . Neither is it less , because then the base BC would be less than the base EF ( Prop . XIII . ) , which is also contrary to the supposition ; therefore , the angle BAC is not less ...
Página 23
... ( Prop . XIII . ) , which is also contrary to the hypothesis . Therefore , the angle A must be equal to the angle D ... ( Prop . II . , Cor . 1 ) ; therefore , two sides and the included angle of one triangle , are equal to two sides and the ...
... ( Prop . XIII . ) , which is also contrary to the hypothesis . Therefore , the angle A must be equal to the angle D ... ( Prop . II . , Cor . 1 ) ; therefore , two sides and the included angle of one triangle , are equal to two sides and the ...
Página 24
... ( Prop . II . , Cor . 1 ) ; therefore two sides and the included angle of one triangle , are equal to two sides and the included angle of the other triangle ; hence the side CF is equal to the side CA ( Prop . VI . ) . But the straight ...
... ( Prop . II . , Cor . 1 ) ; therefore two sides and the included angle of one triangle , are equal to two sides and the included angle of the other triangle ; hence the side CF is equal to the side CA ( Prop . VI . ) . But the straight ...
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Términos y frases comunes
ABCD allel altitude angle ABC angle ACB angle BAC base bisected chord circle circumference cone convex surface cosine curve described diagonals diameter dicular divided draw ellipse equal angles equal to AC equiangular equilateral equivalent exterior angle figure foci four right angles frustum given angle given point greater hyperbola hypothenuse inscribed intersect Join latus rectum less Let ABC logarithm major axis mean proportional meet multiplied number of sides opposite ordinate parabola parallelogram parallelopiped pendicular perimeter perpen perpendicular plane MN principal vertex prism PROPOSITION pyramid quadrant radii radius ratio rectangle regular polygon right angles right angles Prop right-angled triangle Scholium secant segment side AC similar sine solid angle sphere spherical triangle square subtangent tang tangent THEOREM triangle ABC vertex vertices
Pasajes populares
Página 20 - The circumference of every circle is supposed to' be divided into 360 equal parts, called degrees ; each degree into 60 minutes, and each minute into 60 seconds. Degrees, minutes, and seconds are designated by the characters °, ', ". Thus 23° 14' 35" is read 23 degrees, 14 minutes, and 35 seconds.
Página 148 - The radius of a sphere, is a straight line drawn from the center to any point of the surface.
Página 18 - BC common to the two triangles, which is adjacent to their equal angles ; therefore their other sides shall be equal, each to each, and the third angle of the one to the third angle of the other, (26.
Página 34 - ... 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 to BD.
Página 32 - 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 159 - If two triangles have two angles and the included side of the one, equal to two angles and the included side of the other, each to each, the two triangles will be equal.
Página 44 - A Circle is a plane figure bounded by a curved line every point of which is equally distant from a point within called the center.
Página 30 - 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.
Página 29 - If a straight line is perpendicular to one of two parallel lines, it is perpendicular to the other also.
Página 151 - But when a solid angle is formed by three plane angles, the sum of any two of them is greater than the third (Prop.