 | New Jersey. State Board of Education - 1888 - 694 σελίδες
...that similar triangles are to one another as the squares of their homologous sides ? 4. Prove that in the same circle, or in equal circles, equal chords are equally distant from the center. 5. Show how to find the center of a given circle. 6. A road runs round a circular shrubbery... | |
 | 1889 - 584 σελίδες
...lines. In a given circle find the points equidistant from two given intersecting straight lines. 2. In the same circle or in equal circles equal chords are...the greater is nearer to the centre than the less. Through a given point within a circle draw the shortest possible chord. 3. If two circles meet at a... | |
 | James Wallace MacDonald - 1889 - 80 σελίδες
...points not in a straight line, to draw a circumference through them. Proposition IX. A Theorem. 172. In the same circle, or in equal circles, equal chords are equally distant from the centre ; and conversely, chords equally distant from the centre are equal. .5^ Book I., Proposition XXXVIII. Proposition... | |
 | George Albert Wentworth - 1889 - 264 σελίδες
...Corollary. If two circumferences have three points common, they coincide throughout. 85. Theorem. In the same circle, or in equal circles, equal chords are equally distant from the centre; and conversely. 86. Theorem. In the same circle, or in equal circles, of two unequal chords the greater... | |
 | George Albert Wentworth - 1889 - 276 σελίδες
...Corollary. If two circumferences have three points common, they coincide throughout. 85. Theorem. In the same circle, or in equal circles, equal chords are equally distant from the centre; and conversely. 86. Theorem. In the same circle, or in equal circles, of two unequal chords the greater... | |
 | James Wallace MacDonald - 1894 - 76 σελίδες
...Propositions XVIII. and XIX. II. Given a circumference, to find its centre. Proposition IX. A Theorem. 172. In the same circle, or in equal circles, equal chords are equally distant from the centre ; and conversely, chords equally distant from the centre are equal. See Book I., Proposition XXXVIII. Proposition... | |
 | Edward Albert Bowser - 1890 - 420 σελίδες
...parallel chords in a circle is the diameter perpendicular to these chords. Proposition 6. Theorem. 206. In the same circle, or in equal circles, equal chords are equally distant from the centre; and conversely, chords •which are equally distant from the centre are equal to one another. (1) Hyp.... | |
 | William Chauvenet - 1893 - 340 σελίδες
...of parallel chords is the diameter perpendicular to the chords. PROPOSITION VII.—THEOREM. 18. In the same circle, or in equal circles, equal chords...distant from the centre ; and of two unequal chords, the less is at the greater distance from the centre. 1st. Let AB, CD, be equal chords; OE, OF, the perpendiculars... | |
 | George Albert Wentworth, George Anthony Hill - 1894 - 150 σελίδες
...are equal when the three sides of one are equal respectively to the three sides of the other. 2. In the same circle, or in equal circles, equal chords are equally distant from the centre. 3. If AC and BC are tangents to a circle whose centre is O, from a point C without the circle, prove... | |
 | Charles Ambrose Van Velzer, George Clinton Shutts - 1894 - 416 σελίδες
...a JL to the common chord at its middle point and extend both ways. PROPOSITION XI. THEOREM. 153. In the same circle, or in equal circles, equal chords are equally distant from the center, and of two unequal chords the greater is nearer the center. I. Let AB and CD represent equal... | |
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In the same circle, or in equal circles, equal chords are equally distant from the centre ; and of two unequal chords, the less is at the greater distance from the centre. 
