The Contents of the Fifth and Sixth Books of EuclidThe University Press, 1900 - 143 sider |
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Side vi
... Euclid's Fifth Book so very difficult . There is first the difficulty arising out of Euclid's notation for magnitudes and numbers . This has been entirely removed in most modern editions by using an algebraic notation and need not ...
... Euclid's Fifth Book so very difficult . There is first the difficulty arising out of Euclid's notation for magnitudes and numbers . This has been entirely removed in most modern editions by using an algebraic notation and need not ...
Side vii
... Euclid's First Axiom it is difficult to see the need for a proof . This only becomes apparent when the reader realises that Euclid's procedure may be described thus : - Let A , B , C , D be four magnitudes satisfying the conditions of ...
... Euclid's First Axiom it is difficult to see the need for a proof . This only becomes apparent when the reader realises that Euclid's procedure may be described thus : - Let A , B , C , D be four magnitudes satisfying the conditions of ...
Side viii
... Euclid's line of argument , arising from the fact that he uses the Seventh Definition where the Fifth alone need be employed . His Fifth Definition states the conditions which must be satisfied in order that two ratios may be the same ...
... Euclid's line of argument , arising from the fact that he uses the Seventh Definition where the Fifth alone need be employed . His Fifth Definition states the conditions which must be satisfied in order that two ratios may be the same ...
Side ix
... Euclid's Test for Equal Ratios as stated in the Fifth Definition of the Fifth Book . It is the one which springs most naturally out of the nature of the subject . It contains three classes of alternatives , one of which appears only ...
... Euclid's Test for Equal Ratios as stated in the Fifth Definition of the Fifth Book . It is the one which springs most naturally out of the nature of the subject . It contains three classes of alternatives , one of which appears only ...
Side x
Euclid, Micaiah John Muller Hill. multiple scale of two magnitudes is , then to prove a few of the simpler properties of ... Euclid's argument it is not made clear what a ratio is ; and the lack of information on this point is a serious ...
Euclid, Micaiah John Muller Hill. multiple scale of two magnitudes is , then to prove a few of the simpler properties of ... Euclid's argument it is not made clear what a ratio is ; and the lack of information on this point is a serious ...
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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.