Elements of GeometryHilliard and Metcalf, at the University Press, 1819 - 208 pages |
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Page iii
... corollaries , & c . , in one continued series . Moreover the work is considered as divided into two parts , one treating of plane figures and the other of solids ; and the subdivisions of each part are denominated sec- tions . The ...
... corollaries , & c . , in one continued series . Moreover the work is considered as divided into two parts , one treating of plane figures and the other of solids ; and the subdivisions of each part are denominated sec- tions . The ...
Page 3
... Corollary is a consequence which follows from one or sev- eral propositions . A Scholium is a remark upon one or more propositions which have gone before , tending to show their connexion , their restric- tion , their extension , or the ...
... Corollary is a consequence which follows from one or sev- eral propositions . A Scholium is a remark upon one or more propositions which have gone before , tending to show their connexion , their restric- tion , their extension , or the ...
Page 5
... Corollary 1. If one of the angles ACD , BCD , is a right angle , the other is also a right angle . 30. Corollary II . If the line DE ( fig . 18 ) is perpendicular to Fig . 18 . AB ; reciprocally , AB is also perpendicular to DE . For ...
... Corollary 1. If one of the angles ACD , BCD , is a right angle , the other is also a right angle . 30. Corollary II . If the line DE ( fig . 18 ) is perpendicular to Fig . 18 . AB ; reciprocally , AB is also perpendicular to DE . For ...
Page 7
... Corollary . When , in two triangles , these three things are equal , namely , the angle AD , the side AB DE , and the side AC = DF , we may thence infer , that the other three are also equal , namely , the angle BE , the angle CF , and ...
... Corollary . When , in two triangles , these three things are equal , namely , the angle AD , the side AB DE , and the side AC = DF , we may thence infer , that the other three are also equal , namely , the angle BE , the angle CF , and ...
Page 8
... Corollary . When , in two triangles , these three things are equal , namely , BC = EF , B = E , and C = F , we may thence infer that the other three are also equal , namely , AB = DE , AC = DF , and A = D. THEOREM . 40. One side of a ...
... Corollary . When , in two triangles , these three things are equal , namely , BC = EF , B = E , and C = F , we may thence infer that the other three are also equal , namely , AB = DE , AC = DF , and A = D. THEOREM . 40. One side of a ...
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Common terms and phrases
ABCD adjacent angles algebraic algebraic quantities altitude angle ACB base centre chord circ circle circular sector circumference coefficient common divisor cone consequently contains Corollary cube cylinder Demonstration denominator denoted diameter divided dividend division equal equivalent evident example exponent expression factors figure fraction frustum given gives greater greatest common divisor homologous sides inscribed less letters logarithm manner measure multiplied obtain parallel parallelogram parallelopiped perpendicular plane MN polyedron preceding prism proportion proposed equation proposition quotient radical sign radii radius ratio rectangle reduced regular polygon remainder result right angles Scholium side BC similar solid angle sphere spherical square root straight line substitute subtract suppose term THEOREM third tion triangle ABC triangular pyramids unity unknown quantity vertex whence
Popular passages
Page 63 - The square of the hypothenuse is equal to the sum of the squares of the other two sides ; as, 5033 402+302.
Page 7 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Page 151 - THE sphere is a solid terminated by a curve surface, all the points of which are equally distant from a point within, called the centre.
Page 76 - 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.
Page 25 - Two equal chords are equally distant from the centre ; and of two unequal chords, the less is at the greater distance from the centre.
Page 52 - The sum of the squares on the sides of a parallelogram is equal to the sum of the squares on the diagonals.
Page 160 - If two triangles have two sides and the inchtded angle of the one respectively equal to two sides and the included angle of the other, the two triangles are equal in all respects.
Page 203 - In every triangle the sum of the three angles is equal to two right angles.
Page 162 - In any spherical triangle, the greater side is opposite the greater angle ; and conversely, the greater angle is opposite the greater side.
Page 141 - If a pyramid is cut by a plane parallel to its base, the...