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 iii
... called out many works by able mathematicians and skillful teachers . Professor Hayward , of Harvard University , as early as 1825 , defined parallel lines as lines having the same direc- tion . Euclid's definitions of a straight line ...
... called out many works by able mathematicians and skillful teachers . Professor Hayward , of Harvard University , as early as 1825 , defined parallel lines as lines having the same direc- tion . Euclid's definitions of a straight line ...
Σελίδα 9
... called a PROPO- SITION . Every proposition contains the subject of which the assertion is made , and the property or circumstance asserted . When the subject has some condition attached to it , the proposition is said to be conditional ...
... called a PROPO- SITION . Every proposition contains the subject of which the assertion is made , and the property or circumstance asserted . When the subject has some condition attached to it , the proposition is said to be conditional ...
Σελίδα 10
... called a COROLLARY . This term is also frequently applied to propositions , the demonstration of which is very brief and simple . 4. The reasoning by which a proposition is proved is called the DEMONSTRATION . The explanation how a ...
... called a COROLLARY . This term is also frequently applied to propositions , the demonstration of which is very brief and simple . 4. The reasoning by which a proposition is proved is called the DEMONSTRATION . The explanation how a ...
Σελίδα 13
... called the FOURTH PROPORTIONAL of the other three . A series of equal ratios is written , a b c d e f , etc. When a series of quantities is such that the ratio of each to the next following is the same , they are written , a b c d , etc ...
... called the FOURTH PROPORTIONAL of the other three . A series of equal ratios is written , a b c d e f , etc. When a series of quantities is such that the ratio of each to the next following is the same , they are written , a b c d , etc ...
Σελίδα 16
... called proportion by COMPOSITION . 24. Proposition . The difference between the first and second terms of a proportion is to the second , as the dif- ference between the third and fourth is to the fourth . The given proportion , a : b ...
... called proportion by COMPOSITION . 24. Proposition . The difference between the first and second terms of a proportion is to the second , as the dif- ference between the third and fourth is to the fourth . The given proportion , a : b ...
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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.