The Contents of the Fifth and Sixth Books of EuclidThe University Press, 1900 - 143 σελίδες |
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Αποτελέσματα 1 - 5 από τα 30.
Σελίδα xiv
... corresponding segments of the other straight line . 14. Given three segments of straight lines , to find a fourth ... angles at the centres are proportional to the arcs on which they stand . ( 2 ) angles at the circumferences are ...
... corresponding segments of the other straight line . 14. Given three segments of straight lines , to find a fourth ... angles at the centres are proportional to the arcs on which they stand . ( 2 ) angles at the circumferences are ...
Σελίδα xvi
... parts by a perpendicular drawn from the vertex of the right angle on to the hypotenuse ... sides of the triangle . ( ii ) If the base of a triangle be divided ... corresponding to the Arithmetical Theorem X S 36. If A : B = B : C , 37. If ...
... parts by a perpendicular drawn from the vertex of the right angle on to the hypotenuse ... sides of the triangle . ( ii ) If the base of a triangle be divided ... corresponding to the Arithmetical Theorem X S 36. If A : B = B : C , 37. If ...
Σελίδα xvii
... sides . ( It may be equal , and then a circle can be described through the vertices of the quadrilateral . ) The ... corresponding sides . 45. ( i ) If A : B = C : D , then figure on A : similar and similarly described figure on B ...
... sides . ( It may be equal , and then a circle can be described through the vertices of the quadrilateral . ) The ... corresponding sides . 45. ( i ) If A : B = C : D , then figure on A : similar and similarly described figure on B ...
Σελίδα 41
... angles at the circumference of the same or of equal circles is the same as that of the arcs on which they stand . [ Prop . 10 . ( iii ) The proof of this is derivable from that of ( i ) by replacing therein each arc by the corresponding ...
... angles at the circumference of the same or of equal circles is the same as that of the arcs on which they stand . [ Prop . 10 . ( iii ) The proof of this is derivable from that of ( i ) by replacing therein each arc by the corresponding ...
Σελίδα 51
... equal angles being defined as corresponding sides , the ratio of any pair of corresponding sides must be equal to the ratio of every other pair of corresponding sides . 2 Let A , B , C , D , E1 , A2 B2C2D2E2 be two similar figures ...
... equal angles being defined as corresponding sides , the ratio of any pair of corresponding sides must be equal to the ratio of every other pair of corresponding sides . 2 Let A , B , C , D , E1 , A2 B2C2D2E2 be two similar figures ...
Άλλες εκδόσεις - Προβολή όλων
The Contents of the Fifth and Sixth Books of Euclid Euclid,Micaiah John Muller Hill Πλήρης προβολή - 1900 |
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 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.
Σελίδα 99 - Prove that similar triangles are to one another in the duplicate ratio of their homologous sides.
Σελίδα 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...
Σελίδα 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...
Σελίδα xvi - In a right triangle, if a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I.
Σελίδα 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...
Σελίδα 84 - If they do not intersect, show that the radical axis is perpendicular to the line joining the centres of the circles...
Σελίδα 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.
Σελίδα 80 - If four straight lines be proportionals, the rectangle contained by the extremes is equal to the rectangle contained by the means.