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 10
... hence the Latin name of this method of reasoning - reductio ad absurdum . A work on Geometry consists of definitions , proposi- tions , demonstrations , and solutions , with introductory or explanatory remarks . Such remarks sometimes ...
... hence the Latin name of this method of reasoning - reductio ad absurdum . A work on Geometry consists of definitions , proposi- tions , demonstrations , and solutions , with introductory or explanatory remarks . Such remarks sometimes ...
Σελίδα 30
... Hence , two straight lines have the same form , and can differ from each other only in their extent ( 37 ) . 74. Any straight line may be diminished in any ratio ( 67 ) , and may therefore be divided in any ratio . The points in two ...
... Hence , two straight lines have the same form , and can differ from each other only in their extent ( 37 ) . 74. Any straight line may be diminished in any ratio ( 67 ) , and may therefore be divided in any ratio . The points in two ...
Σελίδα 32
... Hence , a stretched cord is used for marking straight lines . The word straight is derived from " stretch , " of which it is an obsolete participle . ANGLES . 82. An ANGLE is the difference in direction of two lines which have a common ...
... Hence , a stretched cord is used for marking straight lines . The word straight is derived from " stretch , " of which it is an obsolete participle . ANGLES . 82. An ANGLE is the difference in direction of two lines which have a common ...
Σελίδα 40
... Hence , AF is longer than AC , or AE , or any line from A meeting the given line at a less distance from D than DF . 111. Corollary . - A point may be at the same distance from two points of a straight line , one on each side of the ...
... Hence , AF is longer than AC , or AE , or any line from A meeting the given line at a less distance from D than DF . 111. Corollary . - A point may be at the same distance from two points of a straight line , one on each side of the ...
Σελίδα 41
... Hence , AD is greater than CD ( 110 ) . The point D is supposed to be in the plane of ACD . If it were not , the perpendicular from it might fall on the point B. BISECTED ANGLE . 113. Theorem . - Every point of the line which bisects an ...
... Hence , AD is greater than CD ( 110 ) . The point D is supposed to be in the plane of ACD . If it were not , the perpendicular from it might fall on the point B. BISECTED ANGLE . 113. Theorem . - Every point of the line which bisects an ...
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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.