Elementary Course of Geometry ...Harper & brothers, 1847 - 103 páginas |
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Página 6
... half the circle , or a segment cut off by a diameter . A Semicir- cumference is half the circumference . 48. A Sector is a part of a circle which is bounded by an arc , and two radii . Note . - A sector is a surface , as is also a ...
... half the circle , or a segment cut off by a diameter . A Semicir- cumference is half the circumference . 48. A Sector is a part of a circle which is bounded by an arc , and two radii . Note . - A sector is a surface , as is also a ...
Página 29
... half the par- allelogram . Let ABCD be a parallelogram , and D ABE a triangle , on the same base AB , and between the same parallels AB , DE ; then will the parallelogram ABCD be double the triangle ABE , or the triangle half the ...
... half the par- allelogram . Let ABCD be a parallelogram , and D ABE a triangle , on the same base AB , and between the same parallels AB , DE ; then will the parallelogram ABCD be double the triangle ABE , or the triangle half the ...
Página 30
Charles William Hackley. ABE is also equal to half the same parallelogram ABCD . Q. E. D. Corol . A triangle is equal to half a parallelogram of the same base and altitude . THEOREM XXIV . The complements of the parallelograms which are ...
Charles William Hackley. ABE is also equal to half the same parallelogram ABCD . Q. E. D. Corol . A triangle is equal to half a parallelogram of the same base and altitude . THEOREM XXIV . The complements of the parallelograms which are ...
Página 31
... half of it . Q. E. D. THEOREM XXVI . In any right - angled triangle , the square of the hy- pothenuse is equal to the sum of the squares of the other two sides . Let ABC be a right - angled triangle , having the right angle A ; then ...
... half of it . Q. E. D. THEOREM XXVI . In any right - angled triangle , the square of the hy- pothenuse is equal to the sum of the squares of the other two sides . Let ABC be a right - angled triangle , having the right angle A ; then ...
Página 34
... half base , is equal to the sum of the squares of the other two sides . Let ABC be a triangle , and CD the line drawn from the vertex to the middle of the base AB , bisecting it into the two equal parts AD , DB ; then will the sum of ...
... half base , is equal to the sum of the squares of the other two sides . Let ABC be a triangle , and CD the line drawn from the vertex to the middle of the base AB , bisecting it into the two equal parts AD , DB ; then will the sum of ...
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Términos y frases comunes
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
Pasajes populares
Página 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.
Página 70 - The areas or spaces of circles are to each other as the squares of their diameters, or of their radii.
Página 50 - Proportional, when the ratio of the first to the second is equal to the ratio of the second to the third.
Página 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.
Página 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.
Página 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.
Página 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.
Página 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.
Página 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.
Página 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.