Elements of GeometryHarper & brothers, 1896 - 540 sider |
Inni boken
Resultat 1-5 av 92
Side 23
... prove that there cannot be two straight lines between X and X ' . The parallel axiom ( viz .: that through a point ... proved that we can never get rid of the parallel axiom without assuming the space in which we live to be very ...
... prove that there cannot be two straight lines between X and X ' . The parallel axiom ( viz .: that through a point ... proved that we can never get rid of the parallel axiom without assuming the space in which we live to be very ...
Side 25
... proved correct after reaching § 104. ] PROPOSITION X. THEOREM 43. If two straight lines are cut by a third straight line , making the alternate - interior angles equal , the lines are par- allel . GIVEN TO PROVE b A- α a = a ' . AB and ...
... proved correct after reaching § 104. ] PROPOSITION X. THEOREM 43. If two straight lines are cut by a third straight line , making the alternate - interior angles equal , the lines are par- allel . GIVEN TO PROVE b A- α a = a ' . AB and ...
Side 28
... PROVE A b C- D AB and CD parallel . b = AOP . Suppose XY to be a line drawn through O , making XOP = b . Then XY is parallel to CD . $ 43 [ If two straight lines are cut by a third straight line , making the alternate- interior angles ...
... PROVE A b C- D AB and CD parallel . b = AOP . Suppose XY to be a line drawn through O , making XOP = b . Then XY is parallel to CD . $ 43 [ If two straight lines are cut by a third straight line , making the alternate- interior angles ...
Side 32
... PROVE ABC , any triangle , with a , b , and c its angles . a + b + c = 2 right angles . Draw KH parallel to BC , and from O , any point of this line , draw OE and CD parallel respectively to the sides AB and AC . * This was first proved ...
... PROVE ABC , any triangle , with a , b , and c its angles . a + b + c = 2 right angles . Draw KH parallel to BC , and from O , any point of this line , draw OE and CD parallel respectively to the sides AB and AC . * This was first proved ...
Side 36
... PROVE the angle B equals the angle C. Suppose AD to be a line bisecting the angle A. On AD as an axis revolve the ... proved in the preceding demonstration . 73. COR . II . The line joining the middle 36 PLANE GEOMETRY.
... PROVE the angle B equals the angle C. Suppose AD to be a line bisecting the angle A. On AD as an axis revolve the ... proved in the preceding demonstration . 73. COR . II . The line joining the middle 36 PLANE GEOMETRY.
Innhold
3 | |
15 | |
32 | |
60 | |
66 | |
81 | |
85 | |
106 | |
287 | |
288 | |
308 | |
326 | |
335 | |
345 | |
351 | |
353 | |
108 | |
154 | |
160 | |
170 | |
180 | |
193 | |
196 | |
202 | |
229 | |
235 | |
246 | |
257 | |
270 | |
282 | |
360 | |
366 | |
378 | |
390 | |
413 | |
456 | |
493 | |
500 | |
508 | |
515 | |
523 | |
529 | |
538 | |
Andre utgaver - Vis alle
Vanlige uttrykk og setninger
ABCD allel altitude angles are equal apothem base and altitude bisecting bisector centre chord circumference circumscribed coincide cone conical surface construct cylinder Def.-The Defs.-A diagonals diameter diedral angles distance divided draw drawn equilateral triangle equivalent Exercise.-The face angles figure Find the area frustum given line given point given straight line GIVEN TO PROVE given triangle Hence homologous homologous sides hypotenuse intersection lateral area lateral edges lateral faces locus measured by arc middle points number of sides parallel planes parallelogram parallelopiped pass a plane perimeter PLANE GEOMETRY plane MN polyedral angle polyedron prismatic surface Q. E. D. PROPOSITION quadrilateral radii radius ratio of similitude rectangle regular polygon right angles right triangle segment similar slant height sphere spherical polygon square surface symmetrical tangent tetraedron THEOREM triangle ABC triangles are equal triangular prism triedral vertex vertices volume
Populære avsnitt
Side 180 - Two triangles which have an angle of one equal to the supplement of an angle of the other are to each other as the products of the sides including the supplementary angles.
Side 5 - If of three quantities the first is greater than the second and the second greater than the third, then the first is greater than the third.
Side 434 - The area of a zone is equal to the product of its altitude by the circumference of a great circle.
Side 393 - 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...
Side 185 - To construct a square equivalent to the sum of any number of given squares.
Side 390 - Two triangles are congruent if (a) two sides and the included angle of one are equal, respectively, to two sides and the included angle of the other...
Side 67 - The straight line joining the middle points of two sides of a triangle is parallel to the third side, and equal to half of it.
Side 70 - The three medians of any triangle intersect in a common point which is two-thirds of the distance from each vertex to the middle of the opposite side.
Side 476 - The area of any regular polygon inscribed in a circle is a mean proportional between the areas of the inscribed and circumscribed polygons of half the number of sides.
Side 71 - The perpendiculars from the vertices of a triangle to the opposite sides meet in a point.