 | Abram Robertson - 1825 - Liczba stron: 180
...but in the hyperbola C P1-C Q1=C P2-DP x PE =s (6. ii.) C D1 =*C Ea. BOOK 200. In an ellipse the sum of the squares of any two .conjugate diameters is equal to the sum of the squares PROP- of the axes ; but in an hyperbola the difference of the Fig. 83, 84. squares... | |
 | Edinburgh encyclopaedia - 1830 - Liczba stron: 828
...drawn, is equal to the square of CA, the semidiameter. Fer CE1-r.CG'=CE«+AE.En=CAl. COR. 3. The sum of the squares of any two conjugate diameters, is equal to the sum of the squares of ihe axes. Let Aa, B6 be the axes, and Pp, Qtf any two conjugate diameters ; tlraw... | |
 | Henry Parr Hamilton - 1834 - Liczba stron: 272
...contained by the Segments of the other 144 J-, SECT. II. On the Properties of Conjugate Diameters. The Sum of the Squares of any two Conjugate Diameters is equal to the Sum of the Squares of the Axes 146. The Area of Circumscribing Parallelograms, whose sides are Parallel... | |
 | Ireland commissioners of nat. educ - 1834 - Liczba stron: 370
...to the sum of the squares of the ordinates drawn from the conjugate to the axis, . . . .92 The sum of the squares of any two conjugate diameters is equal to the sum of the squares of the transverse and conjugate diameters, . . .93 The sum of the squares of any... | |
 | Henry Parr Hamilton - 1834 - Liczba stron: 240
...Segments of the other ................ 144 SECT. II. On the Properties of Conjugate Diameters. The Sum of the Squares of any two Conjugate Diameters is equal to the Sum of the Squares of the Axes ................ 146 The Area of Circumscribing Parallelograms, rvkose... | |
 | Charles Davies - 1836 - Liczba stron: 370
...CP'-PT'-A^-B*, A'*-PT!'=A8-B". Now, it has already been proved, that the difference of the squares of the two conjugate diameters is equal to the difference of the squares of the axes (Prop. VIII, Sch. 11). But A and B are the semi-axes, and A' is a semi-diameter: hence, PT must... | |
 | William Wallace - 1837 - Liczba stron: 248
...the square of CR the semi-diameter. For CE* + CG* = CE* + RE • E/- = CR* (5, 2, E.) COR. 3. The sum of the squares of any two conjugate diameters is equal to the sum of the squares of the axes. Let Rr, Ss be the axes, and Pp, Qq any two conjugate diameters ; draw... | |
 | A. Bell - 1837 - Liczba stron: 180
...to the segments intercepted on CG from C by perpendiculars on it from Q and D. COR. 3. — The sum of the squares of any two conjugate diameters is equal to the sum of the squares of the transverse and conjugate axis. For CD2 + CQ2 = CK2 + KD2 + CN2 + NQ2 = (CK2... | |
 | 1837 - Liczba stron: 136
...drawn from the vertices of two semi-conjugates to the axis. Cor. 6. From this it appears Chat the sum of the squares of any two conjugate diameters is equal to the sum of the squares of the transverse and conjugate diameters. For Ac2 + cD2 = (N O2 + R X2 + cX2 +... | |
 | Charles Davies - 1838 - Liczba stron: 366
...A* - B*, A'*-PTf=At-B*. Now, it has already been proved, that the difference of the squares of the two conjugate diameters is equal to the difference of the squares of the axes (Prop. VIII, Sch. 11). But A and B are the semi-axes, and A' is a semi-diameter: hence, PT must... | |
| |
Fig. 83,84. conjugate diameters is equal to the sum of the squares of the... 
