A new supplement to Euclid's Elements of geometry, by the author of 'A new introduction to the mathematics'.Whittaker & Company, 1840 - 84 páginas |
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Página 11
... bisect the angle bcd by the line ce ( 1 Euclid , 9 ) ; the right- angle acb will be trisected by the lines cd and ce ; that is , the three angles at the vertex c , will be equal to each other . For ( by 1 Euclid , 32 ) the three Α ...
... bisect the angle bcd by the line ce ( 1 Euclid , 9 ) ; the right- angle acb will be trisected by the lines cd and ce ; that is , the three angles at the vertex c , will be equal to each other . For ( by 1 Euclid , 32 ) the three Α ...
Página 12
... bisected in ce , the three angles acd , dce , and ecb , which compose the whole right - angle acb , are equal angles ; wherefore the right - angle acb is trisected in the lines cd and ce , which was to be done . Note . - A right - angle ...
... bisected in ce , the three angles acd , dce , and ecb , which compose the whole right - angle acb , are equal angles ; wherefore the right - angle acb is trisected in the lines cd and ce , which was to be done . Note . - A right - angle ...
Página 15
... bisect the right - angle acb by the line ce ( by 1 Euclid , 9 ) , cutting the line ab in e . From the point a as a centre , and at the dis- tance ae , describe the circle efg , cutting the cir- cumference of the circle abd in the point ...
... bisect the right - angle acb by the line ce ( by 1 Euclid , 9 ) , cutting the line ab in e . From the point a as a centre , and at the dis- tance ae , describe the circle efg , cutting the cir- cumference of the circle abd in the point ...
Página 21
... bisected in the point i ; and because bi is half of bh , it is equal to half of the side bc , which is equal to bh . In like manner it may be demonstrated that the base ai is equal to the base ic ; that is , that ac is bisected in i ...
... bisected in the point i ; and because bi is half of bh , it is equal to half of the side bc , which is equal to bh . In like manner it may be demonstrated that the base ai is equal to the base ic ; that is , that ac is bisected in i ...
Página 22
... bisect the vertical angle . Let the triangle abc be an isosceles triangle , and let the base be bisected in the point d ; the right line db , which d C joins the point of bisection d and the vertex b of the triangle abc opposite to the ...
... bisect the vertical angle . Let the triangle abc be an isosceles triangle , and let the base be bisected in the point d ; the right line db , which d C joins the point of bisection d and the vertex b of the triangle abc opposite to the ...
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A New Supplement to Euclid's Elements of Geometry, by the Author of 'a New ... Joseph Denison Sin vista previa disponible - 2015 |
Términos y frases comunes
ae is equal angle abc angle acb angle bad angles cab arc adc bisected centre circle abcd circle age circle klmn clid contains 30 Corollary demonstrated describe a square describe the circle describe the square diagonal diameter ac double the square duplicate ratio equal angles equal sides equal to 60 equal to half equi equilateral triangle given circle abd given circle efgh given line given right line given square abcd half the given hexagon homologous sides hypothenuse isosceles triangle join Let abcd multiple octuple Proposition 14 quadruple the square radii radius ac rectangles ac remaining angle right-angle acb Scholium sextuple side ab side ac similar polygon inscribed similar triangles spaces described square abfg square bdih square described square efgh square gikl square of ac subtend Supplement triangle abc trigon abc trigon inscribed triple the square trisected vertical angle wherefore the angle wherefore the square
Pasajes populares
Página 62 - Similar triangles are to one another in the duplicate ratio of their homologous sides.
Página 5 - The areas of two similar triangles are to one another as the squares of their homologous or similarly situated sides (fig.
Página 41 - PROP. XV. THEOR. Magnitudes have the same ratio to one another which their equimultiples have. Let AB be the same multiple of C, that DE is of F: C shall be to F, as AB to DE.
Página 63 - Ratios that are the same to the same ratio, are the same to one another.
Página 39 - F is of B, and that magnitudes have the same ratio to one another which their equimultiples have; (v.
Página 13 - PQ the given straight line, and A the given point in it. It Is required to describe a circle to touch ihe 0 DEB, and also to touch PQ at A.
Página 56 - In any triangle the square on a side opposite to an acute angle is less than the sum of the squares on the sides which contain the acute angle ; (e}. In an obtuse-angled triangle the square on the side subtending the obtuse angle is greater than the sum of the squares on the sides containing...
Página 57 - PROPOSITION 20. In a circle the angle at the centre is double of the angle at the circumference, when the angles have the same circumference as base.
Página 63 - CE equal to the ratio of the square of AB to the square of AD.
Página 61 - And in continued proportions, the square of the mean is equal to the rectangle contained by the extremes.