Elements of Geometry and Conic SectionsHarper & brothers, 1860 - 234 sider |
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Side 21
... ( Prop . VIII . ) ; it is , therefore , less than AB . Conversely , if the side AB is greater than the side AC , ther 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 , ther 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 ...
Side 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 ...
Side 23
... ( Prop . XIII . ) , which is also contrary to the hypothesis Therefore , the angle A must be equal to the angle D. I ... ( Prop . II . , Cor . 1 ) ; therefore , two sides and the included angle of one triangle , are equal to two sides and ...
... ( Prop . XIII . ) , which is also contrary to the hypothesis Therefore , the angle A must be equal to the angle D. I ... ( Prop . II . , Cor . 1 ) ; therefore , two sides and the included angle of one triangle , are equal to two sides and ...
Side 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 ...
Side 26
... ( Prop . XVII . ) , and it has been proved to be equal , which is impossible . Hence BC is not unequal to EF , that is , it is equal to it ; and the triangle ABC is equal to the triangle DEF ( Prop . XV . ) . Therefore , if two right ...
... ( Prop . XVII . ) , and it has been proved to be equal , which is impossible . Hence BC is not unequal to EF , that is , it is equal to it ; and the triangle ABC is equal to the triangle DEF ( Prop . XV . ) . Therefore , if two right ...
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Vanlige uttrykk og setninger
ABCD AC is equal allel altitude angle ABC angle ACB angle BAC base BCDEF bisected 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 angle 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 right angles Prop right-angled triangle Scholium segment side AC similar solid angle sphere spherical triangle square subtangent tangent THEOREM triangle ABC vertex vertices
Populære avsnitt
Side 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.
Side 60 - Any two rectangles are to each other as the products of their bases by their altitudes.
Side 11 - A rhombus, is that which has all its sides equal, but its angles are not right angles.
Side 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.
Side 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.
Side 20 - therefore, because in the triangles DBC, ACB, DB is equal to AC, and BC common to both, the two sides, DB, BC are equal to the two AC, CB, each to each ; and the angle DBC is equal to...
Side 15 - Wherefore, when a straight line, &c. QED PROP. XIV. THEOR. If, at a point in a straight line, two other straight lines, upon the opposite sides of it, make the adjacent angles together equal to two right angles, these two straight lines shall be in one and the same straight line.
Side 148 - It will be shown (p. 7,) that every section of a sphere, made by a plane, is a circle...
Side 14 - The angles which one straight line makes with another upon one side of it, are either two right angles, or are together equal to two right angles.
Side 152 - THEOREM. The sum of the sides of a spherical polygon is less than the circumference of a great circle.