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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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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845
...angles, the centre of the circle is in the line which bisects the other. PROPOSITION II. THEOREM. If any two points be taken in the circumference of a...line drawn from A to B shall fall within the circle. c For if AB do not fall within the circle, let it fall, if possible, without, as AEB ; find D the centre...
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The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - 1845 - 352 sider
...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. 1) 11 the centre...
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The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846
...right angles, the centre of the circle is in the line which bisects the other. PHOP. II. THEOR. If any two points be taken in the circumference of a...drawn from A to B shall fall within the circle. For if not, let it fall, if possible, without, as AEB : find D the centre of the circle ABC ; and join DA,...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1846 - 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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The definitions, postulates, axioms, and enunciations of the propositions of ...

Euclides - 1848
...right angles, the centre of the circle is in the line which bisects the other. PROP. II. THEOREM. If any two points be taken in the circumference of a...line which joins them shall fall within the circle. PROP. III. THEOREM. If a straight line drawn through the centre of a circle, bisect a straight line...
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The first three books of Euclid's Elements of geometry, with theorems and ...

Euclides, Thomas Tate - 1849 - 108 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...not, let it fall, if possible, without, as AEB ; find (in. 1.) D, the centre of the circle ABC, and join AD, DB; in the circumference AB take any point F,...
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The synoptical Euclid; being the first four books of Euclid's Elements of ...

Euclides - 1853
...angles, the centre of the circle is in the line which bisects the other. PROP. II. — THEOREM. If any two points be taken in the circumference of a...line drawn from A to B shall fall within the circle. EB For if AB do not fall within the circle, let it fall, if possible, without, as AEB; find (HI. 1.)...
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The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

Royal Military Academy, Woolwich - 1853
...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...line drawn from A to B shall fall within the circle. Forifitdo not, let it fall, if possible, without, as AEB: find (1. in.) D the centre of the circle...
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The first six books of the Elements of Euclid, with numerous exercises

Euclides - 1853 - 147 sider
...circumference of a circle, the straigli.t line which joins them sliaufau within the, circle. LET abС be a circle, and a. b any two points in the circumference...not, let it fall, if possible, without, as aeb , find (i. 3) d the centre of the circle ab С ; and join ad, db, and produce df, any straight line meeting...
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The Elements of Euclid. Books I.-VI.; XI. 1-21 XII. 1-2. A New Text ..., Bok 1

Euclides - 1853
...line produced. PEOP. II. THEOE. If any two points be taken in the circumference of a circle : then the straight line which joins them shall fall within...circle, and A, B any two points in the circumference. . Then the straight line AB, which joins them, shall fall within the circle. For if it do not fall...
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