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 14
... clid ) ; and because the right line ab joins the two points a and b in the circumference of the cir- cle abd , the right line ab ( by the definition above ) is a chord of ( that is , within ) the circle ; and because the triangle abc is ...
... clid ) ; and because the right line ab joins the two points a and b in the circumference of the cir- cle abd , the right line ab ( by the definition above ) is a chord of ( that is , within ) the circle ; and because the triangle abc is ...
Página 16
... clid , 5 ) . But these two angles cab and cba , to- gether with the right - angle , acb , are equal to two right angles ; that is to 90 ° x 2 = 180 ( by 1 Euclid , 32 ) ; take away the right - angle ach 90 ° , and the two equal angles ...
... clid , 5 ) . But these two angles cab and cba , to- gether with the right - angle , acb , are equal to two right angles ; that is to 90 ° x 2 = 180 ( by 1 Euclid , 32 ) ; take away the right - angle ach 90 ° , and the two equal angles ...
Página 24
... clid , 5 ) ; and because , all the interior angles ach , cab , and cba , are together equal to two right - angles ( 1 Euclid , 32 ) = 180 ° ; and the angle acb is = 120 ° ; therefore the angles cab , cba are together = ( 180 ° 120 ...
... clid , 5 ) ; and because , all the interior angles ach , cab , and cba , are together equal to two right - angles ( 1 Euclid , 32 ) = 180 ° ; and the angle acb is = 120 ° ; therefore the angles cab , cba are together = ( 180 ° 120 ...
Página 37
... clid , 4 ) ; wherefore bc ab ichi ; and ( by equality of the triangles hei • and dce ) ( 5 Euclid , 11 ) nately • de : de ic : hi ; wherefore bc ab : dc : de ; and alter- : bc de ab : de.- But be and dc are radii of the two circles abf ...
... clid , 4 ) ; wherefore bc ab ichi ; and ( by equality of the triangles hei • and dce ) ( 5 Euclid , 11 ) nately • de : de ic : hi ; wherefore bc ab : dc : de ; and alter- : bc de ab : de.- But be and dc are radii of the two circles abf ...
Página 43
... clid , 33 ) will be divided into four equal parts , whereof each part shall be one sixtieth part of the whole circumference ; and in the same manner each of the arcs subtended by the remaining four- teen sides of the quindecagon may be ...
... clid , 33 ) will be divided into four equal parts , whereof each part shall be one sixtieth part of the whole circumference ; and in the same manner each of the arcs subtended by the remaining four- teen sides of the quindecagon may be ...
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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.