Plane and Solid GeometryLongmans, Green and Company, 1898 - 210 sider |
Inni boken
Resultat 1-5 av 84
Side 2
... Theorem is a truth requiring demonstration . 14. A Problem is a question proposed for solution . 15. A Postulate ... theorem , axiom , problem , and postulate . 18. A Demonstration is the course of reasoning by which the truth of a ...
... Theorem is a truth requiring demonstration . 14. A Problem is a question proposed for solution . 15. A Postulate ... theorem , axiom , problem , and postulate . 18. A Demonstration is the course of reasoning by which the truth of a ...
Side 3
... theorem . 21. A Scholium is a remark upon one or more propositions . 22. An Hypothesis is a supposition made either ... theorem , or to solve a problem . 25. The Enunciation of a theorem consists of two parts : the Hypothesis , or that ...
... theorem . 21. A Scholium is a remark upon one or more propositions . 22. An Hypothesis is a supposition made either ... theorem , or to solve a problem . 25. The Enunciation of a theorem consists of two parts : the Hypothesis , or that ...
Side 8
... THEOREM . 44. If a straight line meets another straight line , the sum of the adjacent angles is equal to two right angles . Let DC meet AB at C ; then the sum of the angles DCA and DCB is equal to two right angles . At C , let CE be ...
... THEOREM . 44. If a straight line meets another straight line , the sum of the adjacent angles is equal to two right angles . Let DC meet AB at C ; then the sum of the angles DCA and DCB is equal to two right angles . At C , let CE be ...
Side 9
... THEOREM . 48. CONVERSELY , * if the sum of two adjacent angles is equal to two right angles or to a straight angle , their exterior sides lie in the same straight line . D A C Let the sum of the adjacent angles ACD and BCD be equal to ...
... THEOREM . 48. CONVERSELY , * if the sum of two adjacent angles is equal to two right angles or to a straight angle , their exterior sides lie in the same straight line . D A C Let the sum of the adjacent angles ACD and BCD be equal to ...
Side 11
... , how many degrees are there in each ? 7. If the angles BOA , BOC , AOD , and COD are in the ratio of 1 : 2 : 34 , how many degrees are there in each ? PROPOSITION IV . THEOREM . 52. From a point outside § 51. ] 11 RECTILINEAR FIGURES .
... , how many degrees are there in each ? 7. If the angles BOA , BOC , AOD , and COD are in the ratio of 1 : 2 : 34 , how many degrees are there in each ? PROPOSITION IV . THEOREM . 52. From a point outside § 51. ] 11 RECTILINEAR FIGURES .
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Vanlige uttrykk og setninger
ABCD AC² acute angle AD² adjacent adjacent angles altitude angle formed angles are equal apothem arc BC base and altitude bisect bisector called centre chord circumference circumscribed cone cylinder diagonals diameter diedral angles distance divided draw drawn ECDH equally distant equilateral equivalent EXERCISES faces four right angles frustum given point given straight line hence homologous homologous sides hypotenuse inscribed polygon interior angles intersection isosceles triangle join lateral area lateral edges Let ABC lune mean proportional measured by one-half middle point number of sides parallelogram parallelopiped perimeter perpendicular polyedral angle polyedron PROPOSITION XI prove pyramid Q.E.D. PROPOSITION quadrilateral radii radius ratio rectangle rectangular parallelopiped regular polygon right triangle SCHOLIUM segments semiperimeter sphere spherical angle spherical polygon spherical triangle surface tangent THEOREM triangle ABC triangles are equal triangular triangular prism V-ABC vertex vertical angle
Populære avsnitt
Side 46 - PERIPHERY of a circle is its entire bounding line ; or it is a curved line, all points of which are equally distant from a point within called the centre.
Side 105 - ... any two parallelograms are to each other as the products of their bases by their altitudes. PROPOSITION V. THEOREM. 403. The area of a triangle is equal to half the product of its base by its altitude.
Side 82 - If any number of quantities are proportional, any antecedent is to its consequent as the sum of all the antecedents is to the sum of all the consequents. Let a : b = c : d = e :f Now ab = ab (1) and by Theorem I.
Side 192 - A sphere is a solid bounded by a surface all points of which are equally distant from a point within called the centre.
Side 108 - Two triangles having an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles.
Side 146 - A STRAIGHT line is perpendicular to a plane, when it is perpendicular to every straight line which it meets in that plane.
Side 30 - In an isosceles triangle, the angles opposite the equal sides are equal.
Side 80 - In any proportion the terms are in proportion by Composition ; that is, the sum of the first two terms is to the first term as the sum of the last two terms is to the third term.
Side 79 - If the product of two quantities is equal to the product of two others, one pair may be made the extremes, and the other pair the means, of a proportion. Let ad = ос.
Side 148 - Equal oblique lines from a point to a plane meet the plane at equal distances from the foot of the perpendicular ; and of two unequal oblique lines the greater meets the plane at the greater distance from the foot of the perpendicular.