Elementary Geometry: With Applications in MensurationA. S. Barnes & Company, 1850 - 216 Seiten |
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Seite 43
... pass through the centre of the circle ( Th . ii . Cor ) . In like manner , it may be shown that DF passes through the centre of the circle , and since the centre is found in the two lines ED , DF , it will be found at their common inter ...
... pass through the centre of the circle ( Th . ii . Cor ) . In like manner , it may be shown that DF passes through the centre of the circle , and since the centre is found in the two lines ED , DF , it will be found at their common inter ...
Seite 63
... pass through the points A , B , and C. For , the two right angled triangles OAP and OBP have the side AP equal to the side BP , OP common , and the included Problems . angles OPA and OPB equal , being right BOOK II . 63.
... pass through the points A , B , and C. For , the two right angled triangles OAP and OBP have the side AP equal to the side BP , OP common , and the included Problems . angles OPA and OPB equal , being right BOOK II . 63.
Seite 64
... pass through the points B and C. Sch . This problem enables us to describe the circumference of a circle about a given triangle . For , we may consider the vertices of the three angles as the three points through which the circumference ...
... pass through the points B and C. Sch . This problem enables us to describe the circumference of a circle about a given triangle . For , we may consider the vertices of the three angles as the three points through which the circumference ...
Seite 66
... pass through the points D and E. and since the sides of the triangle are perpendicular to the radii OF , OD , OE , they will be tangent to the circum- ference ( Bk . II . Th . v ) . Hence , the circle will be inscribed in the triangle ...
... pass through the points D and E. and since the sides of the triangle are perpendicular to the radii OF , OD , OE , they will be tangent to the circum- ference ( Bk . II . Th . v ) . Hence , the circle will be inscribed in the triangle ...
Seite 125
... In like manner , AB might be proved perpendicular to any other line of the plane PQ , which should pass through B ; aence , it is perpendicular to the plane ( Def . 1 ) . 11 * GEOMETRY . BOOK VI . OF SOLIDS . DEFINITIONS . BOOK V. 125.
... In like manner , AB might be proved perpendicular to any other line of the plane PQ , which should pass through B ; aence , it is perpendicular to the plane ( Def . 1 ) . 11 * GEOMETRY . BOOK VI . OF SOLIDS . DEFINITIONS . BOOK V. 125.
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Häufige Begriffe und Wortgruppen
12 feet ABCD adjacent angles allel altitude angles equal axis base multiplied bisect breadth called centre chains chord circle whose diameter circular sector circumference common cone consequently convex surface cube cylinder decimal dicular divide dodecagon draw entire surface equal altitudes equal Bk equal to half equivalent figure find the area frustum GEOMETRY half the arc half the product hence heptagon homologous sides hypothenuse included angle inscribed intersection length Let ABCD lower base measured by half Mensuration of Surfaces nonagon number of sides opposite angles outward angle parallelogram parallelopipedon pendicular pentagon perimeter perpen perpendicular plane prism PROBLEM quadrilateral radii radius rectangle regular polygon Required the area rhombus right angled triangle right angles Bk S-ABCDE segment slant height sphere square feet squares described straight line tangent THEOREM three sides trapezoid triangle ABC upper base viii
Beliebte Passagen
Seite 48 - After remarking that the mathematician positively knows that the sum of the three angles of a triangle is equal to two right angles...
Seite 10 - If two triangles have two sides, and the included angle of the one equal to two sides and the included angle of the other, each to each, the two triangles are equal in all respects.
Seite 58 - BD then A is said to have the same ratio to B, that C has to D ; or, the ratio of A to B is equal to the ratio of C to D.
Seite 12 - America, but know that we are alive, that two and two make four, and that the sum of any two sides of a triangle is greater than the third side.
Seite 118 - ... cylinder be cut by a plane parallel to the base, the section is a figure parallel and similar to the base. The one point a...
Seite 112 - 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 162 - To find the area of a trapezoid. RULE. Multiply the sum of the parallel sides by the perpendicular distance between them, and then divide the product by two : the quotient will be the area (Bk.
Seite 149 - This pulyedrun may be considered as formed of pyramids, each having for its vertex the centre of the sphere, and for its base one of the faces of the polyedron.
Seite 119 - If a cone be cut by a plane parallel to the base, the section will be a circle.