An Elementary Treatise on Plane and Solid GeometryJ. Munroe and Company, 1847 - 150 σελίδες |
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Σελίδα 12
... fall upon DA , because the right angles CDB and CDA are equal ; the point F will fall upon E , because DF and DE are equal ; and the straight lines CF and CE will coincide . 39. Theorem . A perpendicular measures the short- est distance ...
... fall upon DA , because the right angles CDB and CDA are equal ; the point F will fall upon E , because DF and DE are equal ; and the straight lines CF and CE will coincide . 39. Theorem . A perpendicular measures the short- est distance ...
Σελίδα 16
... falling at once in each of the lines AC and BC , must fall upon their point of intersection C. The triangles will there- fore coincide , and must be equal . 54. Corollary . Hence , when a side and the two adjacent angles of one triangle ...
... falling at once in each of the lines AC and BC , must fall upon their point of intersection C. The triangles will there- fore coincide , and must be equal . 54. Corollary . Hence , when a side and the two adjacent angles of one triangle ...
Σελίδα 18
... fall within the other triangle ACB , as in fig . 19 , be- cause , by § 40 , AD + DB must in this case be less than AC + CB . Secondly . If D falls without ACB , as in fig . 33 , the triangles ACD and BCD are isosceles , since AC is ...
... fall within the other triangle ACB , as in fig . 19 , be- cause , by § 40 , AD + DB must in this case be less than AC + CB . Secondly . If D falls without ACB , as in fig . 33 , the triangles ACD and BCD are isosceles , since AC is ...
Σελίδα 19
... falls within the first triangle as in fig . 19 , we have by § 40 AC + BC > AD + DB ; whence , substracting the equals AC and AD , BCBD . 2. If the point D falls upon the third side as at E , we have at once BC BE . 3. If the point D ...
... falls within the first triangle as in fig . 19 , we have by § 40 AC + BC > AD + DB ; whence , substracting the equals AC and AD , BCBD . 2. If the point D falls upon the third side as at E , we have at once BC BE . 3. If the point D ...
Σελίδα 20
... fall upon CB produced , since the right angles ABG and DEF are equal . An isosceles triangle CAG is thus formed , and AB being per- pendicular to its base , divides it , by § 57 , into the two equal triangles ABC and ABG . 65. Theorem ...
... fall upon CB produced , since the right angles ABG and DEF are equal . An isosceles triangle CAG is thus formed , and AB being per- pendicular to its base , divides it , by § 57 , into the two equal triangles ABC and ABG . 65. Theorem ...
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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