 | John Gibson - 1881 - 64 pages
...with another on one side of it, are either two right angles or together equal to two right angles. 4. If two straight lines cut one another, the vertical or opposite angles are equal. 5. Find a point in a given straight line such that its distances from two given points may... | |
 | Education Ministry of - 1882 - 292 pages
...wholes are unequal. All equal angles fill the same space. (These form one question.) SECTION II. 1. If two straight lines cut one another, the vertical or opposite angles will be equal. Two equal perpendiculars, PA, QB, are drawn to the line AB from points P, Q, on opposite... | |
 | Marianne Nops - 1882 - 278 pages
...ABD = L ABE, which is absurd, &<_•., &c. PROP. XV. — We pass to the third theorem of the group. If two straight lines cut one another, the vertical or opposite angles are equal. The vertical angles are those whose vertices or heads are exactly opposite. In some of the... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1883 - 428 pages
...impossible. Therefore BE is not in the same straight line with CB. And in the same manner it may be shewn that no other can be in the same straight line with it but BD ; therefore BD is in the same straight line with CB. Wherefore, if at a point &c. QED PROPOSITION 15.... | |
 | Stewart W. and co - 1884 - 272 pages
...greater, which is impossible ; therefore BE is not in the same straight line with BC. And, in like manner, it may be demonstrated that no other can be in the...same straight line with it but BD, which therefore is 'm the same straight line with CB. XV. — If two straight lines cut one another, the vertical, or... | |
 | Euclides - 1884 - 94 pages
...greater, which is impossible : therefore is not in the same straight line with And in the same manner it may be demonstrated, that no other can be in the same straight line with it but , which therefore is in the same straight line with . Wherefore, if at a point, &c. ' RELFE BROTHERS'... | |
 | Euclides - 1884 - 182 pages
...greater ; which is impossible. Therefore BE is not in the same straight line with BC. In the same manner, it may be demonstrated that no other can be in the same straight line with it except BD ; therefore BD is in the same straight line with CB. Wherefore, if at a point, &c. QED 50.... | |
 | Woolwich roy. military acad - 1884 - 148 pages
...EXAMINATION. I. EUCLID (Books I.—IV. and VI.). [Great importance will be attached to accuracy.,] 1. If two straight lines cut one another, the vertical, or opposite, angles shall be equal. ABC is a triangle, BD, CE lines drawn making equal angles with BC, and meeting the opposite sides in... | |
 | Education - 1884 - 708 pages
...within the figure to the circumference are equal. That point is called the centre. Prop. I, Book I. 2. If two straight lines cut one another, the vertical, or opposite angles shall be equal. State and prove the corollaries. Prop. 15, Book I. 3. ABC is a triangle right-angled at B, and the... | |
 | Euclides - 1884 - 214 pages
...From the greater of two given straight lines a part may be cut off equal to the less. Proposition XV. If two straight lines cut one another the vertical or opposite angles are equal. Proposition IV. If two triangles have two sides of the one equal to two sides of the other,... | |
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ABD, the less to the greater, which is impossible ; therefore BE is not in the same straight line with BC. 
