Elements of Geometry and Conic SectionsHarper & brothers, 1861 - 234 Seiten |
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Seite 15
... angles CBE , DBE be a right angle . Now the angle CBA is equal to the sum of the two angles CBE , EBA . To each of ... BAC , CAD , DAE , EAF , formed on the same side of the line BF , is equal to two right c angles ; for their sum is ...
... angles CBE , DBE be a right angle . Now the angle CBA is equal to the sum of the two angles CBE , EBA . To each of ... BAC , CAD , DAE , EAF , formed on the same side of the line BF , is equal to two right c angles ; for their sum is ...
Seite 19
... angle B be equal to the angle C. For , conceive the angle BAC to be bisected by the straight line AD ; then , in the two trian- gles ABD , ACD , two sides AB , AD , and the in- cluded angle in the one , are equal to the two B D sides AC ...
... angle B be equal to the angle C. For , conceive the angle BAC to be bisected by the straight line AD ; then , in the two trian- gles ABD , ACD , two sides AB , AD , and the in- cluded angle in the one , are equal to the two B D sides AC ...
Seite 21
... angle , will be greater than the base of the other . Let ABC , DEF be two trian- gles , having two sides of the one equal to two sides of the other , viz .: AB equal to DE , and AC to DF , but the angle BAC greater than the angle EDF ...
... angle , will be greater than the base of the other . Let ABC , DEF be two trian- gles , having two sides of the one equal to two sides of the other , viz .: AB equal to DE , and AC to DF , but the angle BAC greater than the angle EDF ...
Seite 22
... angle BAC be greater than the angle EDF . B C D F For if it is not greater , it must be either equal to it , or less . But the angle BAC is not equal to the angle EDF , because then the base BC would be equal to the base EF ( Prop . VI ...
... angle BAC be greater than the angle EDF . B C D F For if it is not greater , it must be either equal to it , or less . But the angle BAC is not equal to the angle EDF , because then the base BC would be equal to the base EF ( Prop . VI ...
Seite 27
... angles ABD and BAC is equal to two right an- gles . Therefore , the sum of ABD and ABF is equal to the sum of ABD and BAC . Take away the common angle ABD , and the remainder , ABF , is equal to BAC ; that is GBF is equal to GAE . Again , ...
... angles ABD and BAC is equal to two right an- gles . Therefore , the sum of ABD and ABF is equal to the sum of ABD and BAC . Take away the common angle ABD , and the remainder , ABF , is equal to BAC ; that is GBF is equal to GAE . Again , ...
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Häufige Begriffe und Wortgruppen
ABCD AC is equal allel altitude angle ABC angle ACB angle BAC base BCDEF bisected CA² chord circle circumference cone contained convex surface curve described diagonals diameter draw ellipse equal angles equal to AC equally distant equiangular equilateral equivalent exterior angle foci four right angles frustum given point given straight line greater hyperbola hypothenuse inscribed intersect join latus rectum Let ABC lines AC major axis mean proportional measured by half meet number of sides ordinate parabola parallelogram parallelopiped pendicular perimeter perpen perpendicular plane MN principal vertex prism PROPOSITION pyramid quadrant radii radius ratio rectangle regular polygon right angles Prop right-angled triangle Scholium segment side AC similar similar triangles solid angle sphere spherical triangle square subtangent tangent THEOREM triangle ABC vertex vertices
Beliebte Passagen
Seite 27 - 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.
Seite 157 - The sum of the angles of a spherical triangle is greater than two and less than six right angles ; that is, greater than 180° and less than 540°. (gr). If A'B'C' is the polar triangle of ABC...
Seite 60 - Any two rectangles are to each other as the products of their bases by their altitudes.
Seite 63 - IF a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the' rectangle contained by the parts.
Seite 101 - When you have proved that the three angles of every triangle are equal to two right angles...
Seite 10 - CHG; and they are adjacent angles; but when a straight line standing on another straight line makes the adjacent angles equal to one another, each of them is a right angle; and the straight line which stands upon the other is called a perpendicular to it; therefore from the given point C a perpendicular CH has been drawn to the given straight line AB.
Seite 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.
Seite 22 - 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.
Seite 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.
Seite 41 - It follows that either couplet of a proportion may be multiplied or divided by any quantity, and the resulting quantities will be in proportion. And since by...