Chauvenet's Treatise on Elementary GeometryJ. B. Lippincott Company, 1887 - 322 páginas |
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Página 5
... problems are constantly given as exercises for practice in original work . A syllabus , containing the axioms , the postulates , and the captions of the main theorems and corollaries , has been added to aid student and teacher in ...
... problems are constantly given as exercises for practice in original work . A syllabus , containing the axioms , the postulates , and the captions of the main theorems and corollaries , has been added to aid student and teacher in ...
Página 11
... problem is a question proposed for solu- tion . An axiom is a truth assumed as self - evident . A postu- late ( in geometry ) assumes the possibility of the solution of some problem . Theorems , problems , axioms , and postulates are ...
... problem is a question proposed for solu- tion . An axiom is a truth assumed as self - evident . A postu- late ( in geometry ) assumes the possibility of the solution of some problem . Theorems , problems , axioms , and postulates are ...
Página 67
... Problem . To find the greatest common measure of two quantities . The well - known arithmetical process may be ex- tended to quantities of all kinds . Thus , suppose AB and CD are two straight lines whose common measure is required ...
... Problem . To find the greatest common measure of two quantities . The well - known arithmetical process may be ex- tended to quantities of all kinds . Thus , suppose AB and CD are two straight lines whose common measure is required ...
Página 68
... ; i.e. , than AB + BC . Lay off on AC AB ' , equal to AB . Our problem is now reduced to finding a common measure of B'C and AB , or its equal , CB . Erect at B ' a perpendicular B'A ' to AC 68 ELEMENTS OF GEOMETRY .
... ; i.e. , than AB + BC . Lay off on AC AB ' , equal to AB . Our problem is now reduced to finding a common measure of B'C and AB , or its equal , CB . Erect at B ' a perpendicular B'A ' to AC 68 ELEMENTS OF GEOMETRY .
Página 81
... cut the circles are parallel . Suggestion . FED = CEG , ... DBE = CAE . Consider , also , the case where the given circles are internally tangent . F E B G PROBLEMS OF CONSTRUCTION . Heretofore our figures have been assumed BOOK II . 81.
... cut the circles are parallel . Suggestion . FED = CEG , ... DBE = CAE . Consider , also , the case where the given circles are internally tangent . F E B G PROBLEMS OF CONSTRUCTION . Heretofore our figures have been assumed BOOK II . 81.
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.