An Elementary Treatise on Plane and Solid GeometryJ. Munroe and Company, 1847 - 150 σελίδες |
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Σελίδα vi
... isosceles , and scalene triangle ( 45 ) ; right triangle and its hypothenuse ( 46 ) ; square , rectangle ... isosceles triangle ( 55 , 58 ) , Equilateral and equiangular triangle ( 56 , 59 ) , • Line drawn from the vertex to the middle ...
... isosceles , and scalene triangle ( 45 ) ; right triangle and its hypothenuse ( 46 ) ; square , rectangle ... isosceles triangle ( 55 , 58 ) , Equilateral and equiangular triangle ( 56 , 59 ) , • Line drawn from the vertex to the middle ...
Σελίδα xiii
... , 458 ) , 134 Equal sides and angles of isosceles or equilateral spherical tri- angle ( 453-456 ) , · Opposite sides and angles of spherical triangle ( 460 – 462 ) , b 135 136 · Degree of surface ( 463 ) , 464 ) , CONTENTS . xiii.
... , 458 ) , 134 Equal sides and angles of isosceles or equilateral spherical tri- angle ( 453-456 ) , · Opposite sides and angles of spherical triangle ( 460 – 462 ) , b 135 136 · Degree of surface ( 463 ) , 464 ) , CONTENTS . xiii.
Σελίδα 14
... isosceles ( fig . 23 ) , when two only of its sides are equal , and sca- lene ( fig . 24 ) , when no two of its sides are equal . 46. Definitions . A right - triangle is that which has a right angle . The side opposite to the right ...
... isosceles ( fig . 23 ) , when two only of its sides are equal , and sca- lene ( fig . 24 ) , when no two of its sides are equal . 46. Definitions . A right - triangle is that which has a right angle . The side opposite to the right ...
Σελίδα 16
... isosceles triangle the angles opposite the equal sides are equal . Proof . In the isosceles triangle ABC ( fig . 32 ) , let the equal sides be AB and BC . Equal Angles of the Isosceles Triangle . Let the line 16 [ CH . VII . § 55 ...
... isosceles triangle the angles opposite the equal sides are equal . Proof . In the isosceles triangle ABC ( fig . 32 ) , let the equal sides be AB and BC . Equal Angles of the Isosceles Triangle . Let the line 16 [ CH . VII . § 55 ...
Σελίδα 17
... isosceles trian- gle , is perpendicular to the base , and bisects the base . Proof . a . For , on account of the equality of the trian- gles ABD and BCD , AD must be equal to DC . b . Moreover , the angles BDA and BDC are equal , and ...
... isosceles trian- gle , is perpendicular to the base , and bisects the base . Proof . a . For , on account of the equality of the trian- gles ABD and BCD , AD must be equal to DC . b . Moreover , the angles BDA and BDC are equal , and ...
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Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
ABC fig adjacent angles angle BAC arc BC base and altitude bisect centre chord circumference common altitude construct convex surface Corollary DEF fig Definitions denote diameter divided Draw equal arcs equal distances equiangular with respect equilateral equivalent frustum given angle given circle given line given polygon given sides given square gles greater half the product Hence homologous sides hypothenuse infinite number infinitely small Inscribed Angle inscribed circle isosceles Let ABCD line AB fig line BC lines drawn mean proportional number of sides oblique lines parallel lines parallel to BC parallelogram parallelopipeds perimeter perpendicular plane MN polyedron polygon ABCD &c Problem Proof pyramid or cone radii radius rectangles regular polygon right triangle Scholium sector segment side BC similar polygons similar triangles solid angle Solution sphere spherical polygon spherical triangle straight line tangent Theorem triangles ABC triangular prism vertex vertices whence
Δημοφιλή αποσπάσματα
Σελίδα 68 - The perimeters of two regular polygons of the same number of sides, are to each other as their homologous sides, and their areas are to each other as the squares of those sides (Prop.
Σελίδα 127 - Every section of a sphere, made by a plane, is a circle, Let AMB be a section, made by a plane, in the sphere whose centre is C.
Σελίδα 71 - Rectangles of the same altitude are to each other as their bases, and rectangles of the same base are to each other as their altitudes. 245.
Σελίδα 20 - The sum of the three angles of any triangle is equal to two right angles.
Σελίδα xv - The first term of a ratio is called the antecedent, and the second term the consequent.
Σελίδα 83 - ... we suppose the error A to be of any magnitude whatever. 286. Definition. Similar sectors and similar segments are such as correspond to similar arcs. 287. Theorem. Similar sectors are to each other as the squares of their radii. Proof. The similar sectors AOB, A'OB ' (fig. 136) are, by the same reasoning as in t5 97, the same parts of their respective circles, which the angle O= O...
Σελίδα 31 - Theorem. In the same circle, or in equal circles, equal arcs are subtended by equal chords.
Σελίδα 87 - To construct a parallelogram equivalent to a given square, and having the sum of its base and altitude equal to a given line.
Σελίδα 99 - B, from the plane. 320. Theorem. Oblique lines drawn from a point to a plane at equal distances from the perpendicular are equal; and of two oblique lines unequally distant the more remote is the greater.
Σελίδα 78 - Similar triangles are to each other as the squares of their homologous sides. Proof. In the similar .triangles ABC, A'B'C