The Contents of the Fifth and Sixth Books of EuclidThe University Press, 1900 - 143 sider |
Inni boken
Resultat 1-5 av 11
Side 49
... ( equal to L ) measured in the opposite direction to AD ; and this is the only difference in the constructions for the cases K < L , K > L. K L X D A B E Fig . 79 . 7 H. E. If K < L , then E must fall on 89 ] 49 EUCLID , BOOKS V. AND VI .
... ( equal to L ) measured in the opposite direction to AD ; and this is the only difference in the constructions for the cases K < L , K > L. K L X D A B E Fig . 79 . 7 H. E. If K < L , then E must fall on 89 ] 49 EUCLID , BOOKS V. AND VI .
Side 50
... Hence in this case from Euclid's point of view the construction fails , and there is no point corresponding to C. See Note 7 . SECTION V. SIMILAR FIGURES . PROPOSITIONS 25-32 . Art . 50 [ 89 EUCLID , BOOKS V. AND VI .
... Hence in this case from Euclid's point of view the construction fails , and there is no point corresponding to C. See Note 7 . SECTION V. SIMILAR FIGURES . PROPOSITIONS 25-32 . Art . 50 [ 89 EUCLID , BOOKS V. AND VI .
Side 60
... : HA : [ Prop . 22 . but it is given that BA : CA == · ED : DF , .. ED : DF = GA : HA . [ Prop . 10 . But EDGA by construction , .. DF = HA . [ Prop . 21 . Now in the triangles DEF , AGH , DE = 60 [ 107 EUCLID , BOOKS V. AND VI .
... : HA : [ Prop . 22 . but it is given that BA : CA == · ED : DF , .. ED : DF = GA : HA . [ Prop . 10 . But EDGA by construction , .. DF = HA . [ Prop . 21 . Now in the triangles DEF , AGH , DE = 60 [ 107 EUCLID , BOOKS V. AND VI .
Side 81
... construction as in the preceding part of the proposition . The rectangle contained by K and P is the rectangle contained by AB and BE and is therefore ABEF .. The rectangle contained by L and M is the rectangle contained by BC and BD ...
... construction as in the preceding part of the proposition . The rectangle contained by K and P is the rectangle contained by AB and BE and is therefore ABEF .. The rectangle contained by L and M is the rectangle contained by BC and BD ...
Side 87
... construction will give the value of the ratio compounded of AB : AE and AD : AG as the ratio of two lines . Produce EF to cut CD in H. Join AH , and let it cut FG in M. Through M draw PMQ parallel to AD , cutting AB at P and CD at Q ...
... construction will give the value of the ratio compounded of AB : AE and AD : AG as the ratio of two lines . Produce EF to cut CD in H. Join AH , and let it cut FG in M. Through M draw PMQ parallel to AD , cutting AB at P and CD at Q ...
Andre utgaver - Vis alle
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.