Plane and Solid GeometryLongmans, Green and Company, 1898 - 210 σελίδες |
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Σελίδα 23
... mean the three interior angles . SCALENE . ISOSOELES . EQUILATERAL . 67. A Scalene triangle is one of which no two sides are equal . 68. An Isosceles triangle is one of which two sides are equal . 69. An Equilateral triangle is one of ...
... mean the three interior angles . SCALENE . ISOSOELES . EQUILATERAL . 67. A Scalene triangle is one of which no two sides are equal . 68. An Isosceles triangle is one of which two sides are equal . 69. An Equilateral triangle is one of ...
Σελίδα 78
... Means . Thus , in the above proportion , a and d are the extremes , and b and c the means . The first and third terms are ... mean proportional between a and c . PROPOSITION I. 199. If four quantities are in proportion , 78 RATIO AND ...
... Means . Thus , in the above proportion , a and d are the extremes , and b and c the means . The first and third terms are ... mean proportional between a and c . PROPOSITION I. 199. If four quantities are in proportion , 78 RATIO AND ...
Σελίδα 79
... means . Let To prove By definition ( 197 ) , Clearing of fractions , 200. COR . If then ( by 199 ) a : b = c ; d . ad = bc . α с b d ad = bc . Q.E.D. a : b = b : c , b2 = = ac . .. b = √ac . Q.E.D. That is , the mean proportional ...
... means . Let To prove By definition ( 197 ) , Clearing of fractions , 200. COR . If then ( by 199 ) a : b = c ; d . ad = bc . α с b d ad = bc . Q.E.D. a : b = b : c , b2 = = ac . .. b = √ac . Q.E.D. That is , the mean proportional ...
Σελίδα 93
... mean proportional between the seg- ments of the hypotenuse . III . Each side of the right triangle is a mean proportional between the hypotenuse and its adjacent segment . B A F In the right triangle ABC , let BF be drawn from the ...
... mean proportional between the seg- ments of the hypotenuse . III . Each side of the right triangle is a mean proportional between the hypotenuse and its adjacent segment . B A F In the right triangle ABC , let BF be drawn from the ...
Σελίδα 94
... mean proportional between the segments of the diameter . II . The chord drawn from the point to either extremity of the diameter is a mean proportional between the whole diameter and the adjacent segment . EXERCISES . 1. The squares on ...
... mean proportional between the segments of the diameter . II . The chord drawn from the point to either extremity of the diameter is a mean proportional between the whole diameter and the adjacent segment . EXERCISES . 1. The squares on ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 192 - A sphere is a solid bounded by a surface all points of which are equally distant from a point within called the centre.
Σελίδα 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.
Σελίδα 146 - A STRAIGHT line is perpendicular to a plane, when it is perpendicular to every straight line which it meets in that plane.
Σελίδα 30 - In an isosceles triangle, the angles opposite the equal sides are equal.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.