The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh and Twelfth ; the Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected, and Some of Euclid's Demonstrations are Restored ; Also the Book of Euclid's Data, in Like Manner CorrectedDesilver, 1829 - 516 páginas |
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Página 4
... given of compound ratio , and giving an absurd one in place of it , in the 5th Definition of the 6th Book , which ... given , is put in its proper place among the Definitions of the 5th Book , by which the doctrine of compound ratios is ...
... given of compound ratio , and giving an absurd one in place of it , in the 5th Definition of the 6th Book , which ... given , is put in its proper place among the Definitions of the 5th Book , by which the doctrine of compound ratios is ...
Página 173
... given straight line simi- lar to one given , and so on . Which was to be done . PROP . XIX . THEOR . SIMILAR triangles are to one another in the duplicate ratio of their homologous sides . Let ABC , DEF be similar triangles , having the ...
... given straight line simi- lar to one given , and so on . Which was to be done . PROP . XIX . THEOR . SIMILAR triangles are to one another in the duplicate ratio of their homologous sides . Let ABC , DEF be similar triangles , having the ...
Página 186
... given rectilineal C , exceeding by the parallelogram PO , which is similar to D , because PO is similar to EL ( 24. 6. ) Which was to be done . PROP . XXX , PROB . To cut a given straight line in extreme and mean ratio . Let AB be the given ...
... given rectilineal C , exceeding by the parallelogram PO , which is similar to D , because PO is similar to EL ( 24. 6. ) Which was to be done . PROP . XXX , PROB . To cut a given straight line in extreme and mean ratio . Let AB be the given ...
Página 310
... give a general and summary idea of ratio to beginners , by premising this metaphysical definition , to the more accurate defini- tions of ratios that are the same to one another , or one of which is greater , or less than the other : I ...
... give a general and summary idea of ratio to beginners , by premising this metaphysical definition , to the more accurate defini- tions of ratios that are the same to one another , or one of which is greater , or less than the other : I ...
Página 311
... proportion of numbers to one another is defined , and treated of , yet without giving any definition of the ratio of numbers ; though such a definition was as necessary and useful to be given in that book , as in this but indeed there ...
... proportion of numbers to one another is defined , and treated of , yet without giving any definition of the ratio of numbers ; though such a definition was as necessary and useful to be given in that book , as in this but indeed there ...
Otras ediciones - Ver todas
The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ... Robert Simson,Euclid Euclid Sin vista previa disponible - 2018 |
Términos y frases comunes
altitude angle ABC angle BAC base BC BC is equal BC is given bisected centre circle ABCD circumference co-sine cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid ex æquali excess fore given angle given in magnitude given in position given in species given magnitude given ratio given straight line gnomon greater join less Let ABC multiple parallel parallelogram parallelogram AC perpendicular point F polygon prism proportionals proposition Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment sides BA similar sine solid angle solid parallelopipeds square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore
Pasajes populares
Página 9 - Let it be granted that a straight line may be drawn from any one point to any other point.
Página 81 - The angles in the same segment of a circle are equal to one another.
Página 315 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Página 33 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Página 49 - If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part.
Página 96 - If from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.
Página 155 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Página 22 - ANY two angles of a triangle are together less than two right angles.
Página 25 - Let A, B, C be the three given straight lines, of which any two whatever are greater than the third, viz.
Página 24 - Any two sides of a triangle are together greater than the third side.