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 80.
Σελίδα 11
... greater will exceed the remainder of the less . 9. The whole is equal to the sum of all the parts . 10. The whole is greater than a part . EXERCISE . 11. What is the hypothesis of the first axiom ? Ans . If sev- eral quantities are each ...
... greater will exceed the remainder of the less . 9. The whole is equal to the sum of all the parts . 10. The whole is greater than a part . EXERCISE . 11. What is the hypothesis of the first axiom ? Ans . If sev- eral quantities are each ...
Σελίδα 28
... greater and noting the difference . 65. Problem . - A straight line may be multiplied by any number . For several equal lines may be added together . 66. Problem . - A straight line may be divided by another . By repeating the process ...
... greater and noting the difference . 65. Problem . - A straight line may be multiplied by any number . For several equal lines may be added together . 66. Problem . - A straight line may be divided by another . By repeating the process ...
Σελίδα 34
... the sum of the other two ( 9 ) . D A Problem . An angle may be subtracted from a greater one . For the angle ADB is the difference between ADC and BDC . It is equally evident that an angle may be a 34 ELEMENTS OF GEOMETRY .
... the sum of the other two ( 9 ) . D A Problem . An angle may be subtracted from a greater one . For the angle ADB is the difference between ADC and BDC . It is equally evident that an angle may be a 34 ELEMENTS OF GEOMETRY .
Σελίδα 35
... when the angle which they make is a right angle . Two lines are OBLIQUE to each other when they make an angle which is greater or less than a right angle . 90. Corollary . All right angles are equal . For ANGLES . 35.
... when the angle which they make is a right angle . Two lines are OBLIQUE to each other when they make an angle which is greater or less than a right angle . 90. Corollary . All right angles are equal . For ANGLES . 35.
Σελίδα 36
... greater than one right angle and less than the sum of two , is called OBTUSE . Angles greater than the sum of two right angles are rarely used in ele- mentary geometry . When the sum of two angles is equal to a right angle , each is the ...
... greater than one right angle and less than the sum of two , is called OBTUSE . Angles greater than the sum of two right angles are rarely used in ele- mentary geometry . When the sum of two angles is equal to a right angle , each is 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.