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 3
... reason not equivalent to a good demonstration ; which desultory method of some mathematicians is obstructive of the ad- vance of science ; for if some propositions may be received without the usual strict demonstration , why may not ...
... reason not equivalent to a good demonstration ; which desultory method of some mathematicians is obstructive of the ad- vance of science ; for if some propositions may be received without the usual strict demonstration , why may not ...
Página 8
... vitating bodies are as the squares of the times during which they gravitate ; by which inverted method he seems to make the effect occasion its cause . Struck with the circuitous and clumsy reason- ing which he PREFACE .
... vitating bodies are as the squares of the times during which they gravitate ; by which inverted method he seems to make the effect occasion its cause . Struck with the circuitous and clumsy reason- ing which he PREFACE .
Página 9
Joseph Denison. Struck with the circuitous and clumsy reason- ing which he has met with in the Treatises now in use on Mechanics , particularly as regards gravita- tion , the author has been induced to draw up a fresh Treatise on ...
Joseph Denison. Struck with the circuitous and clumsy reason- ing which he has met with in the Treatises now in use on Mechanics , particularly as regards gravita- tion , the author has been induced to draw up a fresh Treatise on ...
Página 18
... acfg , because the bases eg , ga are equal and they stand between the same parallels ae and ci ( 1 Euclid , 36 ) . For the same reason the parallelogram cbhf is = the square acfg ; and the parallelogram ifhd is 18 A NEW SUPPLEMENT.
... acfg , because the bases eg , ga are equal and they stand between the same parallels ae and ci ( 1 Euclid , 36 ) . For the same reason the parallelogram cbhf is = the square acfg ; and the parallelogram ifhd is 18 A NEW SUPPLEMENT.
Página 30
... reason , the square fhik is double the square aefg ; and therefore the quadruple of the square abcd . Also , for the same reason , the square kmnl is double the square fhik ; and therefore the octuple of the given square abcd ...
... reason , the square fhik is double the square aefg ; and therefore the quadruple of the square abcd . Also , for the same reason , the square kmnl is double the square fhik ; and therefore the octuple of the given square abcd ...
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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.