Elements of Geometry, Conic Sections, and Plane TrigonometryHarber & brothers, 1871 - 58 páginas |
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Página 16
... A B C D It is plain that the two lines must co- incide between A and B , for otherwise there would be two straight lines between A and B , which is impossible ( Axiom 11 ) . Suppose , however , that , on being produced , these lines ...
... A B C D It is plain that the two lines must co- incide between A and B , for otherwise there would be two straight lines between A and B , which is impossible ( Axiom 11 ) . Suppose , however , that , on being produced , these lines ...
Página 32
... A B C D Draw the diagonal BC ; then , because AB s parallel to CD , and BC meets them , the alternate angles ABC , BCD are equal to each other ( Prop . XXIII . ) . Also , because AC is parallel to BD , and BC meets them , the alternate ...
... A B C D Draw the diagonal BC ; then , because AB s parallel to CD , and BC meets them , the alternate angles ABC , BCD are equal to each other ( Prop . XXIII . ) . Also , because AC is parallel to BD , and BC meets them , the alternate ...
Página 58
... ABCD , ABEF be placed so that their equal bases shall coin- cide with each other . Let AB be the common D C F ED F C E A B A B base ; and , since the two parallelograms are supposed to have the same altitude , their upper bases , DC ...
... ABCD , ABEF be placed so that their equal bases shall coin- cide with each other . Let AB be the common D C F ED F C E A B A B base ; and , since the two parallelograms are supposed to have the same altitude , their upper bases , DC ...
Página 59
... ABCD will contain seven partial rectangles , while AEFD will contain four ; therefore the rectangle ABCD is to the rectangle AEFD as 7 to 4 , or as AB to AE . The same rea- soning is applicable to any other ratio than that of 7 to 4 ...
... ABCD will contain seven partial rectangles , while AEFD will contain four ; therefore the rectangle ABCD is to the rectangle AEFD as 7 to 4 , or as AB to AE . The same rea- soning is applicable to any other ratio than that of 7 to 4 ...
Página 60
... ABCD AHID :: AB : AH . But , by hypothesis , we have ABCD : AEFD :: AB : AG . FI C EHG . B In these two proportions the antecedents are equal ; there- fore the consequents are proportional ( Prop . IV . , Cor . , B. II . ) and we have ...
... ABCD AHID :: AB : AH . But , by hypothesis , we have ABCD : AEFD :: AB : AG . FI C EHG . B In these two proportions the antecedents are equal ; there- fore the consequents are proportional ( Prop . IV . , Cor . , B. II . ) and we have ...
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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.