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" Ir any two points be taken in the circumference of a circle, the straight line which joins them shall fall within the circle. Let ABC be a circle, and A, B any two points in the circumference ; the straight line drawn from A to B shall fall within the... "
The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ... - Side 54
av Euclid, Robert Simson - 1838 - 416 sider
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - 1837 - 318 sider
...right angles, the centre of the circle is in the line which bisects the other. PROP. II. THEOR. If any two points be taken in the circumference of a...line drawn from A to B shall fall within the circle. Take any point in AB as E ; find D (1. 3.) the centre of the circle ABC; join AD, DB and DE, and let...
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A companion to Euclid: being a help to the understanding and remembering of ...

Euclides - 1837 - 88 sider
...to be false, 4. that F is the centre of the Q. D PROPOSITION II. (Argument ad absurdum). Theorem. If any two points be taken in the circumference of a...line which joins them shall fall within the circle. Steps of the Demonstration, Suppose that AB falls without the Q, and prove, on that supposition, 1....
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - 1837 - 390 sider
...PROP. II. THEOR. THE straight line which joins any two points in the circumference of a circle, falls within the circle. Let ABC be a circle, and A, B any two points in the circumference ; the chord drawn from A to B falls within the circle. Take any point in AB as E; find (III. I.) D the centre...
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Euclid's Elements [book 1-6] with corrections, by J.R. Young

Euclides - 1838
...be bisected by u perpendicular, that perpendicular will pass through the centre. PROP. II. THEOR. If any two points be taken in the circumference of a...circle. For if it do not, let it fall, if possible, tl 3 without, as AEB; find* D the centre of the circle ABC ; and draw DA, DB. In the arc AB take any...
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The Elements of Euclid

Euclid - 1838 - 416 sider
...right angles, the centre of the circle is in the line which bisects the other. PROP. II. THEOR. IF any two points be taken in the circumference of a...circumference ; the straight line drawn from A to C B shall fall within the circle. For, if it do not, let it fall, if possible, without, as AEB; find...
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The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - 1841 - 351 sider
...right angles, the centre of the circle is in the line which bisects the other. PROP. II. THEOR. If any two points be taken in the circumference of a...within the circle. For, if it do not, let it fall, if pos* 1. 3. sible, without, as AEB; find* D the centre of the circle ABC, and join DA, DB. In the circumference...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1842 - 317 sider
...right angles, the centre of the circle is in the line which bisects the other. PROP. II. THEOR. If any two points be taken in the circumference of a...line drawn from A to B shall fall within the circle. Take any point in AB as E ; find D (1. 3.) the centre of the circle ABC ; join AD, DB and DE, and let...
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Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842
...right angles, the centre of the circle is in the line which bisects the other. PROP. II. THEOR. IF any two points be taken in the circumference of a...line which joins them shall fall within the circle. liet ABC be a circle, and A, в any two points in the circumference: the straight line drawn from A...
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Algebra applied to geometry ... By X. Y. Z.

X. Y. Z. - 1843 - 96 sider
...therefore a line drawn from the centre to the middle point of a chord is perpendicular to the chord. 4*. If any two points be taken in the circumference of a circle, the straight line that joins them shall fall within the circle. (Euclid 3, 2.) Let the axis of x be chosen perpendicular...
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Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ...

Euclid - 1845 - 199 sider
...angles, the centre of the circle is in the line which bisects the other. PROPOSITION II. THEOR. — If any two points be taken in the circumference of a...let it fall, if possible, without, as AEB : find* D the centre of the circle ABC ; and join AD, DB, and produce DF, any straight line meeting the circumference...
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