Chauvenet's Treatise on Elementary GeometryJ. B. Lippincott Company, 1887 - 322 páginas |
Dentro del libro
Resultados 1-5 de 34
Página 41
... parallelogram ( C ) , which is bounded by two pairs of parallel sides . B 0 Α The side upon which a parallelogram is supposed to stand and the opposite side are called its lower and upper bases . The perpendicular distance between the ...
... parallelogram ( C ) , which is bounded by two pairs of parallel sides . B 0 Α The side upon which a parallelogram is supposed to stand and the opposite side are called its lower and upper bases . The perpendicular distance between the ...
Página 42
... parallelogram are equal and the opposite angles are equal . Suggestion . Draw a diagonal AC . ACB and CAD are equal , by Proposition XXV . CAB and ACD are equal , by Proposition . XXV . B A D Hence the triangles ABC and ADC are equal ...
... parallelogram are equal and the opposite angles are equal . Suggestion . Draw a diagonal AC . ACB and CAD are equal , by Proposition XXV . CAB and ACD are equal , by Proposition . XXV . B A D Hence the triangles ABC and ADC are equal ...
Página 43
... parallelogram . Suggestion . Draw a diagonal , and prove the two triangles equal . PROPOSITION XXXII . — THEOREM . 63. The diagonals of a parallelogram bisect each other . Suggestion . The triangles AED and BEC are equal , by ...
... parallelogram . Suggestion . Draw a diagonal , and prove the two triangles equal . PROPOSITION XXXII . — THEOREM . 63. The diagonals of a parallelogram bisect each other . Suggestion . The triangles AED and BEC are equal , by ...
Página 44
... parallelogram . parallelograms . Q. E. D. quod erat demonstran- dum ( = which was to be proved ) . O circle . O circles . 65. In arranging a written demonstration , it is well 44 ELEMENTS OF GEOMETRY .
... parallelogram . parallelograms . Q. E. D. quod erat demonstran- dum ( = which was to be proved ) . O circle . O circles . 65. In arranging a written demonstration , it is well 44 ELEMENTS OF GEOMETRY .
Página 47
... a quadrilateral bisect each other , the figure is a parallelogram . C D A B In the quadrilateral ABCD , let the diagonals AD and BC bisect each other . We are to prove ABCD a In the AEB and CED we have and and But BOOK I. 47.
... a quadrilateral bisect each other , the figure is a parallelogram . C D A B In the quadrilateral ABCD , let the diagonals AD and BC bisect each other . We are to prove ABCD a In the AEB and CED we have and and But BOOK I. 47.
Otras ediciones - Ver todas
Chauvenet's Treatise on Elementary Geometry William Chauvenet,William Elwood Byerly Vista completa - 1887 |
Términos y frases comunes
ABCD adjacent angles altitude angles are equal apothem bisects centre chord coincide common cone construct convex Corollary cylinder Definition diagonal diameter dicular diedral angle distance divided draw equal circles equally distant equilateral equivalent Exercise Find the locus frustum given circle given line given point given straight line greater Hence hypotenuse included angle inscribed angle intercepted arcs isosceles triangle lateral area lateral edges mean proportional middle point number of sides parallel lines parallelogram parallelopiped pass a plane pendicular perimeter perpen perpendicular plane angle plane MN plane passed polyedral angle Proposition VI Proposition VII quadrilateral radii radius ratio rectangle regular inscribed regular polygon respectively equal right angles right triangle Scholium secant secant line segment similar slant height sphere spherical polygon spherical triangle square surface tangent tetraedron Theorem triangle ABC triangles are equal triangular prism triedral upper base vertex volume
Pasajes populares
Página 200 - If a straight line is perpendicular to each of two straight lines at their point of intersection, it is perpendicular to the plane of those lines.
Página 133 - The area of a rectangle is equal to the product of its base and altitude.
Página 137 - Two triangles having an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles.
Página 117 - The square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the other two sides.
Página 214 - The acute angle which a straight line makes with its own projection upon a plane is the least angle which it makes with any line of that plane.
Página 113 - If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar.
Página 38 - The sum of the three angles of any triangle is equal to two right angles.
Página 184 - If two triangles have two sides of the one respectively equal to two sides of the other, and the included angles unequal, the triangle which has the greater included angle has the greater third side.
Página 128 - Find the locus of a point the sum of whose distances from two given straight lines is equal to a given constant, k.
Página 52 - 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.