An Elementary Treatise on Plane and Solid GeometryJ. Munroe and Company, 1847 - 150 σελίδες |
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Σελίδα xvii
... Corollary . The terms of a proportion may be transposed in any way , provided the product of the means is retained equal to that of the extremes , and the proportion will not be destroyed . Thus , the preceding proportion gives , by ...
... Corollary . The terms of a proportion may be transposed in any way , provided the product of the means is retained equal to that of the extremes , and the proportion will not be destroyed . Thus , the preceding proportion gives , by ...
Σελίδα xviii
... Corollary . The sum of the antecedents of a proportion is to the sum of its consequents as either antecedent is to its consequent ; and the difference of the antecedents is to the difference of the consequents in the same ratio ...
... Corollary . The sum of the antecedents of a proportion is to the sum of its consequents as either antecedent is to its consequent ; and the difference of the antecedents is to the difference of the consequents in the same ratio ...
Σελίδα 8
... Corollary . If either of the angles APC , APD , BPC , or BPD is a right angle , the other three must also be right angles . d . Scholium . As a straight line has two different direc- tions exactly opposed to each other , it is not ...
... Corollary . If either of the angles APC , APD , BPC , or BPD is a right angle , the other three must also be right angles . d . Scholium . As a straight line has two different direc- tions exactly opposed to each other , it is not ...
Σελίδα 16
... Corollary . 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 ...
... Corollary . 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 ...
Σελίδα 17
... Corollary . An equilateral triangie is also equi- angular . 57. Theorem . The line BD ( fig . 32 ) , which bi- sects the angle B , at the vertex of an isosceles trian- gle , is perpendicular to the base , and bisects the base . Proof ...
... Corollary . An equilateral triangie is also equi- angular . 57. Theorem . The line BD ( fig . 32 ) , which bi- sects the angle B , at the vertex of an isosceles trian- gle , is perpendicular to the base , and bisects the base . Proof ...
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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