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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Αποτελέσματα 1 - 5 από τα 79.
Σελίδα 88
... base . Then the vertex of the angle opposite the base . is the vertex of the triangle . The 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 ...
... base . Then the vertex of the angle opposite the base . is the vertex of the triangle . The 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 ...
Σελίδα 90
... base , it will bisect the angle at the vertex , and be perpendicular to the base . The straight line which has any two of these four con- ditions must have the other two ( 52 ) . UNEQUAL SIDES . 272. Theorem . - When two sides of a ...
... base , it will bisect the angle at the vertex , and be perpendicular to the base . The straight line which has any two of these four con- ditions must have the other two ( 52 ) . UNEQUAL SIDES . 272. Theorem . - When two sides of a ...
Σελίδα 92
... base of an isosceles triangle be double the angle at the vertex , how many degrees in each ? 3. If the angle at the vertex of an isosceles triangle be double one of the angles at the base , what is the angle at the vertex ? 4. To ...
... base of an isosceles triangle be double the angle at the vertex , how many degrees in each ? 3. If the angle at the vertex of an isosceles triangle be double one of the angles at the base , what is the angle at the vertex ? 4. To ...
Σελίδα 100
... base of an isosceles triangle is to one of the other sides as three to two . Find by construction and measure- ment , whether the vertical angle is acute or obtuse . 2. Two right angled triangles are equal , when any 100 ELEMENTS OF ...
... base of an isosceles triangle is to one of the other sides as three to two . Find by construction and measure- ment , whether the vertical angle is acute or obtuse . 2. Two right angled triangles are equal , when any 100 ELEMENTS OF ...
Σελίδα 109
... base , similar to a given triangle . Let this problem be solved by the student . RIGHT ANGLED TRIANGLES . 323. Every triangle may be divided into two right angled triangles , by a perpendicular let fall from one of its vertices upon the ...
... base , similar to a given triangle . Let this problem be solved by the student . RIGHT ANGLED TRIANGLES . 323. Every triangle may be divided into two right angled triangles , by a perpendicular let fall from one of its vertices upon the ...
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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.