Elements of GeometryHilliard and Metcalf, at the University Press, 1819 - 208 σελίδες |
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Σελίδα vi
... entitled the proportions of figures , contains the measure of surfaces , their comparison , the properties of a right - angled triangle , those of equiangular triangles , of similar figures , & c . We shall be found fault vi Preface .
... entitled the proportions of figures , contains the measure of surfaces , their comparison , the properties of a right - angled triangle , those of equiangular triangles , of similar figures , & c . We shall be found fault vi Preface .
Σελίδα 21
... similar reason AB is parallel to CD ; there- fore the quadrilateral ABCD is a parallelogram . THEOREM . 87. If two opposite sides AB , CD ( fig . 44 ) , of a quadrilateral Fig . 44 . are equal and parallel , the two other sides will ...
... similar reason AB is parallel to CD ; there- fore the quadrilateral ABCD is a parallelogram . THEOREM . 87. If two opposite sides AB , CD ( fig . 44 ) , of a quadrilateral Fig . 44 . are equal and parallel , the two other sides will ...
Σελίδα 26
... similar reason ; it will then be in both of these lines at the same time . But two lines can cut each other in only one point ( 32 ) ; there is therefore only one circle , whose circumference can pass through three given points . 108 ...
... similar reason ; it will then be in both of these lines at the same time . But two lines can cut each other in only one point ( 32 ) ; there is therefore only one circle , whose circumference can pass through three given points . 108 ...
Σελίδα 33
... similar reason the angle CAD has for its measure the half of ED ; therefore BAC + CAD , or BAD , has for its measure the half BE + ED , or the half of BD . Let us suppose , in the second place , that the centre C ( fig . 65 ) , Fig . 65 ...
... similar reason the angle CAD has for its measure the half of ED ; therefore BAC + CAD , or BAD , has for its measure the half BE + ED , or the half of BD . Let us suppose , in the second place , that the centre C ( fig . 65 ) , Fig . 65 ...
Σελίδα 43
... similar , but similar figures may be very unequal . 163. In two different circles , similar arcs , similar sectors , simi- lar segments , are such as correspond to equal angles at the centre . Thus , the angle A ( fig . 92 ) being equal ...
... similar , but similar figures may be very unequal . 163. In two different circles , similar arcs , similar sectors , simi- lar segments , are such as correspond to equal angles at the centre . Thus , the angle A ( fig . 92 ) being equal ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 63 - The square of the hypothenuse is equal to the sum of the squares of the other two sides ; as, 5033 402+302.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 52 - The sum of the squares on the sides of a parallelogram is equal to the sum of the squares on the diagonals.
Σελίδα 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.
Σελίδα 203 - In every triangle the sum of the three angles is equal to two right angles.
Σελίδα 162 - In any spherical triangle, the greater side is opposite the greater angle ; and conversely, the greater angle is opposite the greater side.
Σελίδα 141 - If a pyramid is cut by a plane parallel to its base, the...