Treatise on Geometry and Trigonometry: For Colleges, Schools and Private Students. Written for the Mathematical Course of Joseph Ray, M.D.Sargent, Wilson & Hinkle, 1868 - 420 σελίδες |
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Σελίδα 88
... ALTITUDE of the triangle is the distance from the vertex to the base , which is measured by a perpen- dicular let fall on the base produced , if necessary . 264. Corollary . - The altitude of a triangle is equal to the distance between ...
... ALTITUDE of the triangle is the distance from the vertex to the base , which is measured by a perpen- dicular let fall on the base produced , if necessary . 264. Corollary . - The altitude of a triangle is equal to the distance between ...
Σελίδα 118
... altitudes of a triangle , that is , the perpendiculars let fall from the several vertices on the opposite sides , meet in one point . 31. The lines which join the several vertices of a triangle with the centers of the opposite sides ...
... altitudes of a triangle , that is , the perpendiculars let fall from the several vertices on the opposite sides , meet in one point . 31. The lines which join the several vertices of a triangle with the centers of the opposite sides ...
Σελίδα 128
... ALTITUDE of a parallelogram is the distance be- tween the base and the opposite side . Hence , the alti- tude of a ... altitude . That is , if we multiply the number of units of length contained in the base , by the number of those units ...
... ALTITUDE of a parallelogram is the distance be- tween the base and the opposite side . Hence , the alti- tude of a ... altitude . That is , if we multiply the number of units of length contained in the base , by the number of those units ...
Σελίδα 129
... altitude AD are multiples of the same unit of length , for example , four and three . Di- vide AB into four equal ... altitude . In the exam- ple taken , this is three times four , or twelve . The result would be the same , whatever the ...
... altitude AD are multiples of the same unit of length , for example , four and three . Di- vide AB into four equal ... altitude . In the exam- ple taken , this is three times four , or twelve . The result would be the same , whatever the ...
Σελίδα 130
... altitude of the rectangle divided into infi- nitely small and equal parts ; and then proceeding to form infinitesimal squares , as in the former part of the demonstration . If a straight line move in a direction perpendicular to itself ...
... altitude of the rectangle divided into infi- nitely small and equal parts ; and then proceeding to form infinitesimal squares , as in the former part of the demonstration . If a straight line move in a direction perpendicular to itself ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
adjacent angles altitude angles equal apothem axis base bisect chord circle circumference circumscribed coincide cone Corollary Corollary.-The cosine Cotang curved surface cylinder demonstrated diagonals diameter dicular diedral angle distance divided draw equally distant equivalent EXERCISES faces figure formula four right angles frustum functions Geometry given angle given line given point given straight line given triangle greater Hence homologous homologous lines hypotenuse included angle inscribed intersection isosceles join less let fall mantissa measured number of sides opposite sides parallel lines parallelogram parallelopiped perimeter perpen perpendicular plane polyedral polyedron prism Problem.-Given pyramid quadrilateral radius ratio regular polygon respectively equal right angled triangle secant similar similarly arranged slant hight sphere spherical excess spherical polygon spherical triangle square student subtracting symmetrical Tang tangent tetraedrons theorem Theorem.-The triangles are equal triedral trirectangular vertex vertices volume
Δημοφιλή αποσπάσματα
Σελίδα 183 - If two triangles have two sides of the one respectively equal to two sides of the other, and the contained angles supplemental, the two triangles are equal.
Σελίδα 238 - The volume of any parallelopiped is equal to the product of its base by its altitude.
Σελίδα 72 - Problem. — To draw a line through a given point parallel to a given line.
Σελίδα 141 - The square described on the hypothenuse of a right-angled triangle is equivalent to the sum of the squares described on the other two sides.
Σελίδα 91 - Conversely, if two angles of a triangle are equal, the sides opposite them are also equal, and the triangle is isosceles.
Σελίδα 173 - The areas of two circles are to each other as the squares of their radii ; or, as the squares of their diameters. 502. Corollary. — When the radius is unity, the area is expressed by -. 503. Theorem — The area of a sector is measured by half the product of its arc by its radius.
Σελίδα 240 - Corollary — The volume of any pyramid is equal to one-third of the product of its base by its altitude. For any pyramid...
Σελίδα 260 - The sum of the angles of a spherical triangle is greater than two and less than six right angles ; that is, greater than 180° and less than 540°. (gr). If A'B'C' is the polar triangle of ABC...
Σελίδα 137 - The squa/re described on the difference of two straight lines is equivalent to the sum of the squares described on the two lines, diminished by twice the rectangle contained by the lines.
Σελίδα 274 - The areas of the surfaces of two spheres are to each other as the squares of their radii, or as the squares of their diameters.