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If any two points be taken in the circumference of a circle, the straight line which joins them shall fall within the circle.
Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books - Page 110
by Euclid, Edmund Stone - 1765 - 464 pages

## The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - Trigonometry - 1827 - 513 pages
...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 circle, the straight line which joins them shall fall within the circle. Let ABC be a circle, and A, B any two...

## The First Six Books of the Elements of Euclid, with a Commentary and ...

Euclid, Dionysius Lardner - Euclid's Elements - 1828 - 324 pages
...cannot meet a circle in more than two points. PROPOSITION II. THEOREM. (331) If any two points (A and B) be taken in the circumference of a circle, the right line which joins them falls within the circle. For, if it be possible, let AEB be a right line in which the point E is without...

## The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 513 pages
...centre of the circle is in the line which bisects the other. c8. I. dlO.Def.l. PROP. II. THEOR. If any two points be taken in the circumference of a circle, the straight line ivhich joins them must fall within the circle. Let ABC be a circle, and A, B any two...

## Mathematical Problems and Examples, Arranged According to Subjects, from the ...

Mathematics - 1836 - 335 pages
...proportional. 24. Through a given point draw a straight line parallel to 1834 a given straight line. 25. If any two points be taken in the circumference of a circle, the straight line which joins them falls within the circle. 26. Triangles and parallelograms of the same...

## The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

Mathematics - 1836 - 472 pages
...segments of a circle are those in which the angles are equal, or which contain equal angles. PROP. II. If any two points be taken in the circumference of a circle, the straight line which joins them shall fall within the circle. III. If a straight line drawn through...

## Elements of Plane Geometry According to Euclid

Andrew Bell - Euclid's Elements - 1837 - 240 pages
...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 circle, the straight line which joins them shall fall within the circle. Let ABC be a circle, and A, B, any two...

## A companion to Euclid: being a help to the understanding and remembering of ...

Euclides - Euclid's Elements - 1837 - 88 pages
...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 circle, the straight line which joins them shall fall within the circle. Steps of the Demonstration, Suppose that...

## 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, the straight line which joins them shall fall within the circle. Let ABC be a circle, and A, B any two...