 | Edward Atkins - 1874 - 426 σελίδες
...Therefore also BAC is a right angle (Ax. 1). Therefore, if the square, &c. QED EXERCISES. PROP. 1—15. 1. From the greater of two given straight lines to cut off a portion which is three times as long as the less. 2. The line bisecting the vertical angle of an isosceles... | |
 | Euclides, James Hamblin SMITH - 1876 - 382 σελίδες
...21. Ax. 3. Ax. 1. Thus from pt. A a st. line AL has been drawn = BC. 0. EF PROPOSITION III. PROBLEM. From the greater of two given straight lines to cut off a part equal to the less. 1.2. Ax. 1. Let AB be the greater of the two given st. lines AB, CD. Jt is required to cut off from... | |
 | Richard Wormell - 1876 - 268 σελίδες
...line.f .. 84 2. From a given point to draw a straight line equal to a given stra1ght line. .. 28 3. From the greater of two given straight lines to cut off a part equal to the less. 28 7. Upon the same base and on the same side of it, there cannot be two triangles that have their... | |
 | Robert Potts - 1876 - 446 σελίδες
...BG, wherefore AL and .BC are each of them equal to BG ; •td things that are equal to the same thing are equal to one another) therefore the straight line AL is equal to BC. (ax. 1.) Wherefore from the given point A, a straight line AL has been drawn equal to the given straight... | |
 | Henry Major - 1876 - 784 σελίδες
...Account for his unpopularity, and mention the chief disputes in which he was engaged. Euclid. — 1. Prom the greater of two given straight lines to cut off a part eqnal to the less. What are the data and what are the qitcesita in this proposition ? 2. If two straight... | |
 | Edward Atkins - 1876 - 130 σελίδες
...BAC is a right angle (Ax. 1). Therefore, if the square, &c. QED EXERCISES ON BOOK IPROP. 1—15. 1. From the greater of two given straight lines to cut off a portion •Which is three times as long as the less. 2. The line bisecting the vertical angle of an... | |
 | Euclides - 1877 - 58 σελίδες
...3) Now AL and BC are each of them equal to BG, therefore AL and BC are equal to each other. (ax. 1) Wherefore from the given point A a straight line AL has been drawn equal to the given straight line. QEF Exercises. 1. If the radms of the smaller circle be half that of the larger, how fails the given... | |
 | Edward Atkins - 1877 - 72 σελίδες
...are equal to the same thing are equal to one another, therefore AL is equal to BC (Ax. 1). Therefore from the given point A a straight line AL has been drawn equal to the given straight line BC. Which was to be done. Proposition 3.— Problem. from the greater of two given straight lines to cut... | |
 | W J. Dickinson - 1879 - 44 σελίδες
...the given line which is farther removed from it, instead of the nearer one, as in Euclid. 3. Show how from the greater of two given straight lines to cut off a part equal to the less. 4. If two triangles have two sides of the one equal to two sides of the other, each to each, and have... | |
 | Euclides - 1879 - 146 σελίδες
...for each case : this will give eight different examples of this problem.] PROPOSITION III. PROBLEM. From the greater of two given straight lines to cut off a •bart equal to the less. Let AB and CD be the two given st. lines, of which AB is the greater. It... | |
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BC. Wherefore from the given point A a straight line AL has been drawn equal to the given straight line BC. 
