 | John Playfair - 1833 - 346 σελίδες
...taking away the equal rectangles 2BC. CD and 2AC.CD, there re" mains AD2+DB2=2ACH2CD2." PROP. X. THEOR. If a straight line be bisected, and produced to any point, the square of the whole line thus produced, and the square of the part of it produced, are together double... | |
 | Euclides - 1834 - 518 σελίδες
...* parts ; wherefore ABCD is also double of the triangle EBC. Therefore, if a parallelogram, &c. QED given triangle, and have one of its angles equal to a given rectilineal angle. Let ABC be the given triangle, and D the given rectilineal angle ; it is required to describe a parallelogram... | |
 | Euclid - 1835 - 540 σελίδες
...Wherefore, " the complements," &c. QED PROP. XLIV. PROB. To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have...of its angles equal to a given rectilineal angle. Let AB be the given straight line, and C the given triangle, and D the given rectilineal angle. It... | |
 | John Playfair - 1835 - 336 σελίδες
...to the given straight line BC. PROP. XIV. PROB. To describe a parallelogram that shall be equivalent to a given triangle, and have one of its angles equal to a given rectilineal angle. Let ABC be the given triangle, and D the given rectilineal angle. It ia required to describe a parallelogram... | |
 | 1836 - 366 σελίδες
...centre from their common diameter is equal to twice its radius. 39. Define a parallelogram. Describe one which shall be equal to a given triangle, and have...of its angles equal to a given rectilineal angle. 40. Describe a square about a given circle. SECTION II. QUESTIONS IN ARITHMETIC AND ALGEBRA, NOT INCLUDING... | |
 | Robert Mudie - 1836 - 524 σελίδες
...geometrically, or as it applies to lines ; and for this purpose it is usually enunciated in these tcnns : " If a straight line be bisected, and produced to any point ; the square of the whole line thus produced, and the square of the part of it produced, are together double... | |
 | Robert Mudie - 1836 - 542 σελίδες
...geometrically, or as it applies to lines ; and for this purpose it is usually enunciated in these terms : " If a straight line be bisected, and produced to any point ; the square of the whole line thus produced, and the square of the part of it produced, are together double... | |
 | John Playfair - 1836 - 148 σελίδες
...square of CB, is equal to the square of CD. Wherefore, if a straight line, &c. QED PROP. XXIII. THEOR. If a straight line be bisected, and produced to any point, the square of the whole line thus produced*, and the square of the part of it produced, are together double... | |
 | 1836 - 488 σελίδες
...double of the square of half the line, and of the square of the line between the points of section. X. If a straight line be bisected, and produced to any point, the square of the whole line thus produced, and the square of the part of it produced, are together double... | |
 | Andrew Bell - 1837 - 290 σελίδες
...remaining complement KD. PROPOSITION XLIV. PROBLEM. To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have...of its angles equal to a given rectilineal angle. Let AB be the given straight line, and C the given triangle, and D the given rectilineal angle. It... | |
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To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle. 
