Elements of GeometryHilliard and Metcalf, at the University Press, 1819 - 208 σελίδες |
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Σελίδα vi
... According as we advance in geometry , we find it necessary to combine together a greater number of relations , and algebra may be of great service in conducting us to our conclusions by the readiest and most easy method . This work is ...
... According as we advance in geometry , we find it necessary to combine together a greater number of relations , and algebra may be of great service in conducting us to our conclusions by the readiest and most easy method . This work is ...
Σελίδα 8
... according as the point G falls without the triangle ABC , on the side BC , or within the triangle . Case 1. Because GC < GI + IC , and AB < AI + IB , there- fore GC + AB < GI + AI + IC + IB , that is , GC + AB < AG + BC . From one 8 ...
... according as the point G falls without the triangle ABC , on the side BC , or within the triangle . Case 1. Because GC < GI + IC , and AB < AI + IB , there- fore GC + AB < GI + AI + IC + IB , that is , GC + AB < AG + BC . From one 8 ...
Σελίδα 10
... less than B , then according to what has just been demonstrated we should have AB < AC , which is con- trary to the hypothesis ; and if C were equal to B , then it would follow , that AC = AB ( 48 ) , 10 Elements of Geometry .
... less than B , then according to what has just been demonstrated we should have AB < AC , which is con- trary to the hypothesis ; and if C were equal to B , then it would follow , that AC = AB ( 48 ) , 10 Elements of Geometry .
Σελίδα 28
... according to what has just been demonstrated , MH = HP , and MK = KP ; therefore the entire arc HMK = HPK , and it is moreover evident , that each of these arcs is a semicircumfer- ence . Fig . 57 , 58 . THEOREM . 113. If the ...
... according to what has just been demonstrated , MH = HP , and MK = KP ; therefore the entire arc HMK = HPK , and it is moreover evident , that each of these arcs is a semicircumfer- ence . Fig . 57 , 58 . THEOREM . 113. If the ...
Σελίδα 30
... according to what has just been demonstrated , AI DE . But , by hypo- thesis , the arc AB DE ; we should consequently have AI AB , or the part equal to the whole , which is impossible ; therefore the angle ACB DCE . THEOREM . 120. In ...
... according to what has just been demonstrated , AI DE . But , by hypo- thesis , the arc AB DE ; we should consequently have AI AB , or the part equal to the whole , which is impossible ; therefore the angle ACB DCE . THEOREM . 120. In ...
Άλλες εκδόσεις - Προβολή όλων
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...