Elementary Course of Geometry ... |
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Page 12
... Let the two triangles ABC , DEF have the an- gle A equal to the angle D , the angle B equal to the angle E , and the side AB equal to the side DE ; then these two triangles will be B identical . AA СЕ F For , conceive the triangle ABC ...
... Let the two triangles ABC , DEF have the an- gle A equal to the angle D , the angle B equal to the angle E , and the side AB equal to the side DE ; then these two triangles will be B identical . AA СЕ F For , conceive the triangle ABC ...
Page 14
... ABC have the angle C equal to the angle B , it will also have the side AB equal to the side AC . D For if not , let BA be greater than AC , and take BD equal to AC , and join the points C and D by the line CD ; then the two triangles ABC ...
... ABC have the angle C equal to the angle B , it will also have the side AB equal to the side AC . D For if not , let BA be greater than AC , and take BD equal to AC , and join the points C and D by the line CD ; then the two triangles ABC ...
Page 16
... Let the line AB meet the line CD ; then will the two angles ABC , ABD , taken together , be equal to two right angles . C B D For , suppose BE drawn perpen- dicular to CD . Then the two angles CBA , ABD fill the same angular space with ...
... Let the line AB meet the line CD ; then will the two angles ABC , ABD , taken together , be equal to two right angles . C B D For , suppose BE drawn perpen- dicular to CD . Then the two angles CBA , ABD fill the same angular space with ...
Page 17
... Let ABC be a triangle , having the side AB produced to D ; then will the outward angle CBD be greater than either of the inward opposite angles A or C. For , conceive the side BC to be bisected in the point E , and draw the line AE ...
... Let ABC be a triangle , having the side AB produced to D ; then will the outward angle CBD be greater than either of the inward opposite angles A or C. For , conceive the side BC to be bisected in the point E , and draw the line AE ...
Page 18
... Let ABC be a triangle , having the side AB greater than the side BC ; then will the angle ACB , opposite the greater side AB , be greater than the angle A , opposite the less side CB . For , on the greater side ABD take the part BD ...
... Let ABC be a triangle , having the side AB greater than the side BC ; then will the angle ACB , opposite the greater side AB , be greater than the angle A , opposite the less side CB . For , on the greater side ABD take the part BD ...
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Common terms and phrases
ABCD altitude angles equal axis bisect center of similitude chord circumference cone consequently construct cylinder diagonal diameter dicular divided draw equal angles equal bases equal distances equiangular equilateral triangle figure find a point find the area frustum geometric locus given angle given circle given line given point given triangle gles Hence hypothenuse indeterminate problems inscribed intersection isosceles isosceles triangle Let ABC line drawn line joining locus which resolves measured meet parallel planes parallelogram pendicular pentagon perimeter perpen perpendicular plane angles plane XZ polygon polyhedral angle polyhedrons prism Prob Prop proportional Prove pyramid radical axis radii radius ratio rectangle regular polygon regular polyhedrons resolves this problem rhombus right line right-angled triangle Scholium segment semicircle side AC similar Solution sphere spherical polygon spherical triangle straight line surface symmetric tangent tetrahedrons triangle ABC trihedral angles vertex
Popular passages
Page 33 - In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square of the side subtending the obtuse angle, is greater than the squares of the sides containing the obtuse angle, by twice the rectangle contained by the side upon which, when produced, the perpendicular falls, and the straight line intercepted without the triangle, between the perpendicular and the obtuse angle.
Page 70 - The areas or spaces of circles are to each other as the squares of their diameters, or of their radii.
Page 50 - Proportional, when the ratio of the first to the second is equal to the ratio of the second to the third.
Page 50 - Four quantities are said to be proportional when the ratio of the first to the second is the same as the ratio of the third to the fourth.
Page 60 - Carol. 4. Parallelograms, or triangles, having an angle in each equal, are in proportion to each other as the rectangles of the sides which are about these equal angles. THEOREM LXXXII. IF a line be drawn in a triangle parallel to one of its sides, it will cut the other two sides proportionally.
Page 23 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Page 1 - A straight line is said to be perpendicular to a plane when it is perpendicular to every straight line which passes through its foot in that plane, and the plane is said to be perpendicular to the line.
Page 51 - Proportion, when the ratio is the same between every two adjacent terms, viz. when the first is to the second, as the second to the third, as the third to the fourth, as the fourth to the fifth, and so on, all in the same common ratio.
Page 5 - ... 07958 in using the circumferences j then taking one-third of the product, to multiply by the length, for the content. Ex. 1. To find the number of solid feet in a piece of timber, whose bases are squares, each side of the greater end being 15 inches, and each side of the less end 6 inches ; also, the length or perpendicular altitude 2-1 feet.
Page 2 - What is the upright surface of a triangular pyramid, the slant height being 20 feet, and each side of the base 3 feet ? • Ans.