An Elementary Treatise on Plane and Solid GeometryJ. Munroe and Company, 1847 - 150 σελίδες |
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Σελίδα 16
... Hence , when two sides and the included angle of one triangle are respectively equal to those of another , the other side and angles are also equal in the two triangles . 53. Theorem . Two triangles are equal , when a side and the two ...
... Hence , when two sides and the included angle of one triangle are respectively equal to those of another , the other side and angles are also equal in the two triangles . 53. Theorem . Two triangles are equal , when a side and the two ...
Σελίδα 18
... Hence and ACD = ADC , BCD BDC ; - but this is impossible ; for of the first members of these equations ACD > BCD while of the second members ADC BDC . 61. Theorem . When two triangles are equilateral with respect to each other , they ...
... Hence and ACD = ADC , BCD BDC ; - but this is impossible ; for of the first members of these equations ACD > BCD while of the second members ADC BDC . 61. Theorem . When two triangles are equilateral with respect to each other , they ...
Σελίδα 19
... Hence BD CD - AD + DB = AD + DC . AD + DC AB > AC . AC 2. Conversely . Suppose AB > AC , the angle C must be greater than B ; for if C were equal to or less than B , AB would by § 61 and the preceding demonstration , be equal to or less ...
... Hence BD CD - AD + DB = AD + DC . AD + DC AB > AC . AC 2. Conversely . Suppose AB > AC , the angle C must be greater than B ; for if C were equal to or less than B , AB would by § 61 and the preceding demonstration , be equal to or less ...
Σελίδα 20
... Hence the sum of the three angles of the triangle is equal to ACB + BCE + ECD , or , by § 25 , to two right angles . 66. Corollary . Two angles of a triangle being given , or only their sum , the third will be known by subtract- ing the ...
... Hence the sum of the three angles of the triangle is equal to ACB + BCE + ECD , or , by § 25 , to two right angles . 66. Corollary . Two angles of a triangle being given , or only their sum , the third will be known by subtract- ing the ...
Σελίδα 25
... Hence , all the radii of a circle are equal , and all its diameters are also equal , and double of the radius . 88. Theorem . Every diameter , as BD ( fig . 43 ) , bi- sects the circle and its circumference . Proof . For if the figure ...
... Hence , all the radii of a circle are equal , and all its diameters are also equal , and double of the radius . 88. Theorem . Every diameter , as BD ( fig . 43 ) , bi- sects the circle and its circumference . Proof . For if the figure ...
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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