The Elements of EuclidLongmans, Green and Company, 1866 - 376 páginas |
Dentro del libro
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Página 172
... Ratio is a mutual relation of two magnitudes of the same kind to one another in respect of quantity . IV . Magnitudes are said to have a ratio to one an- other , when the less can be multiplied so as to exceed the other . v . The first ...
... Ratio is a mutual relation of two magnitudes of the same kind to one another in respect of quantity . IV . Magnitudes are said to have a ratio to one an- other , when the less can be multiplied so as to exceed the other . v . The first ...
Página 173
... ratio than the third has to the fourth , and the third is said to have to the fourth a less ratio than the first has to the second . VIII . Analogy , or proportion , is the similitude of ratios . IX . Proportion consists in three terms ...
... ratio than the third has to the fourth , and the third is said to have to the fourth a less ratio than the first has to the second . VIII . Analogy , or proportion , is the similitude of ratios . IX . Proportion consists in three terms ...
Página 174
... ratio which A has to D ; then , for shortness ' sake , M is said to have to N the ratio compounded of the ratios of E to F , G to H , and K to L. XII . In proportionals , the antecedent terms are said to be homologous to one another ...
... ratio which A has to D ; then , for shortness ' sake , M is said to have to N the ratio compounded of the ratios of E to F , G to H , and K to L. XII . In proportionals , the antecedent terms are said to be homologous to one another ...
Página 179
... ratio to the second which the third has to the fourth , and if of the first and third there be taken any equimultiples whatever , and also any whatever of the second and fourth , then the multiple of the first shall have the same ratio ...
... ratio to the second which the third has to the fourth , and if of the first and third there be taken any equimultiples whatever , and also any whatever of the second and fourth , then the multiple of the first shall have the same ratio ...
Página 180
... ratio to the second and fourth , and , in like manner , the first and the third shall have the same ratio to any equimultiples whatever of the second and fourth . Let A the first have to B the second , the same ratio which C , the third ...
... ratio to the second and fourth , and , in like manner , the first and the third shall have the same ratio to any equimultiples whatever of the second and fourth . Let A the first have to B the second , the same ratio which C , the third ...
Términos y frases comunes
AB² ABCD AC² AD² adjacent angles angle ABC angle ACB angle BAC angle equal base BC BC is equal centre chord circle ABC circumference diameter double draw equal angles equal to F equiangular equilateral triangle equimultiples exterior angle fore given circle given line given point given rectilineal given straight line gnomon hypotenuse inscribed intersection isosceles triangle join less Let ABC lines be drawn lines drawn meet multiple opposite angles parallel to BC parallelogram perpendicular plane polygon PROB produced proportionals Q. E. D. PROP rectangle contained rectilineal figure remaining angle right angles segment semicircle shew shewn square on AC tangents THEOR touches the circle triangle ABC twice the rectangle vertex Wherefore