The Contents of the Fifth and Sixth Books of EuclidThe University Press, 1900 - 143 sider |
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Side viii
... scale of the two magnitudes . The notation employed to exhibit it is substantially due to Professor A. E. H. Love , F.R.S. This notation attaches a graphical representation to the Fifth Definition , which appeals to the eye of the ...
... scale of the two magnitudes . The notation employed to exhibit it is substantially due to Professor A. E. H. Love , F.R.S. This notation attaches a graphical representation to the Fifth Definition , which appeals to the eye of the ...
Side ix
... scales ( or two ratios ) . [ See Prop . VIII . ( i ) , ( ii ) . ] The first form of the conditions is Euclid's Test for Equal Ratios as stated in the Fifth Definition of the Fifth ... scale of two magnitudes is , then to prove PREFACE . ix.
... scales ( or two ratios ) . [ See Prop . VIII . ( i ) , ( ii ) . ] The first form of the conditions is Euclid's Test for Equal Ratios as stated in the Fifth Definition of the Fifth ... scale of two magnitudes is , then to prove PREFACE . ix.
Side x
... scale , but also a ratio ; so that he sees why , whenever two relative multiple scales are the same , Euclid expressed that fact in the statement that the ratio of the magnitudes determining the first relative multiple scale is the same ...
... scale , but also a ratio ; so that he sees why , whenever two relative multiple scales are the same , Euclid expressed that fact in the statement that the ratio of the magnitudes determining the first relative multiple scale is the same ...
Side xi
... scales are enunciated from both these points of view . In the part of the book which precedes the section on ratio ( Arts . 62--70 ) , these propositions are enunciated first as properties of relative multiple scales , and secondly as ...
... scales are enunciated from both these points of view . In the part of the book which precedes the section on ratio ( Arts . 62--70 ) , these propositions are enunciated first as properties of relative multiple scales , and secondly as ...
Side xii
... scale as two whole numbers . Prop . 12 relates to differing relative multiple scales ; and with Props . 9 and 11 is very useful in developing the idea of ratio . Props . 24 , 59 , 60 and 63 appear here chiefly but not entirely on ...
... scale as two whole numbers . Prop . 12 relates to differing relative multiple scales ; and with Props . 9 and 11 is very useful in developing the idea of ratio . Props . 24 , 59 , 60 and 63 appear here chiefly but not entirely on ...
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The Contents of the Fifth and Sixth Books of Euclid (with a Note on ... Euclid Uten tilgangsbegrensning - 1908 |
The Contents of the Fifth and Sixth Books of Euclid Euclid,Micaiah John Muller Hill Uten tilgangsbegrensning - 1900 |
Vanlige uttrykk og setninger
ABCD ABEF angle equal angles reciprocally proportional BCGE BCHD BEFG BEHC bisected BLNO centre circle corresponding sides cross-ratio cutting AC DÊE definition divided drawn perpendicular duplicate ratio ENUNCIATION EQPS equal angles equimultiples Euclid's EXAMPLE exhibited in Fig expressed by Fig fact exhibited four harmonic points four straight lines greater Hence by Prop Hence the triangles hypotenuse integer inversion kind locus mean proportional middle point parallel to BC parallelogram PQRST PROPOSITION Proposition 48 rA rB rA sC radical axis ratio compounded ratio of equality rect rectangle contained relative multiple scale required to prove respectively equal right angle segments shows the fact side BC side corresponding similar figures similar triangles similarly described square on AB square on AC supplementary angles tangents three magnitudes triangle ABC triangle DEF triangles are similar vertex
Populære avsnitt
Side 99 - IF two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proportionals : the triangles shall be equiangular, and shall have those angles equal which are opposite to the homologous sides.
Side xviii - Wherefore, in equal circles &c. QED PROPOSITION B. THEOREM If the vertical angle of a triangle be bisected by a straight line which likewise cuts the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight line which bisects the angle.
Side 99 - Prove that similar triangles are to one another in the duplicate ratio of their homologous sides.
Side xvi - If the vertical angle of a triangle be bisected by a straight line which also cuts the base, the segments of the base shall have the same ratio which the other sides of the triangle have to one another...
Side 99 - ABC, DEF have one angle in the one equal to one angle in the other, viz. the angle BAC to the angle EDF, and the sides about...
Side xvi - In a right triangle, if a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I.
Side 35 - The first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken, and any equimultiples whatsoever of the second and fourth ; if the multiple of the first be less than that of the second, the multiple of the third is also less than that of the fourth: or, if the multiple of the first be equal to that of the second, the multiple of the third is also equal to that of the fourth : or, if...
Side 84 - If they do not intersect, show that the radical axis is perpendicular to the line joining the centres of the circles...
Side 100 - If an angle of a triangle be bisected by a straight line, which likewise cuts the base; the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square of the straight line bisecting the angle.
Side 80 - If four straight lines be proportionals, the rectangle contained by the extremes is equal to the rectangle contained by the means.