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" If two circles touch each other internally, the straight line which joins their centres, being produced, shall pass through the point of contact. "
Practical geometry for art students - Page 41
by John Carroll (art master.) - 1881
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Trigonometry - 1806 - 546 pages
...circle cannot cut another in more than two points. QED PROP. XI. THEOR. IF two circles touch each other internally, the straight line which joins their centres...produced shall pass through the point of contact. Let the two circles ABC, ADE touch each other internally in the point A, and let F be the centre of...
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Pantologia. A new (cabinet) cyclopędia, by J.M. Good, O. Gregory ..., Volume 5

John Mason Good - 1813 - 714 pages
...circle cannot cut another in more than two points. Prop. XI. Theor. If two circles touch each other internally, the straight line which joins their centres...produced shall pass through the point of contact. Prop. XII. Theor. If two circles touch each other externally, the straight line which joins their centres...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 588 pages
...circle cannot cut another in more than two points. QED PROP. XI. THEOR. IF two circles touch each other internally, the straight line which joins their centres...produced shall pass through the point of contact. Let the two circles ABC, ADE touch each other internally in the point A, and let F be the centre of...
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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - Trigonometry - 1827 - 546 pages
...circle cannot cut another in more than two points. QED PROP. XL THEOR. If two circles touch each other internally, the straight line which joins their centres...produced shall pass through the point of contact. Let the two circles ABC, ADE touch each other internally in the point A; and let F be the centre of...
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Elements of Plane Geometry According to Euclid

Andrew Bell - Euclid's Elements - 1837 - 290 pages
...one another, which is impossible (III. 5). PROPOSITION XI. THEOREM. If two circles touch each other internally, the straight line which joins their centres...produced, shall pass through the point of contact. Let the two circles ABC, ADE, touch each other internally in the point A, and let F be the centre of...
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A companion to Euclid: being a help to the understanding and remembering of ...

Euclides - Euclid's Elements - 1837 - 112 pages
...supposition is false. PROPOSITION XI. (Argument ad absurdum). Theorem. If two circles touch each other internally, the straight line which joins their centres,...produced, shall pass through the point of contact. Steps of the Demonstration. Suppose that the line which joins the centres does not pass through the...
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Euclid's Elements [book 1-6] with corrections, by J.R. Young

Euclides - 1838 - 264 pages
...circumference of a circle cannot cut another in more than two points. QED PROP. XI. THEOR. If one circle touch another internally, the straight line which joins...centres being produced shall pass through the point uf contact. Let the circle ADE touch the circle ABC internally both preserved in several modern editions,...
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The Elements of Euclid

Euclid - Geometry - 1838 - 470 pages
...circle cannot cut another in more than two points. QED PROP. £L THEOR. IF two circles touch each other internally the straight line which joins their centres being produced shall pass through thfe point of contact. Let the two circles ABC, ADE touch each other internally in the point A, and...
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Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842 - 316 pages
...circle cannot cut another in more than two points. QED PROP. XI. THEOR. IF two circles touch each other internally, the straight line which joins their centres...produced shall pass through the point of contact. Let the two circles ABC, ADE touch each other internally in the point A, and let F be the centre of...
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The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - Geometry - 1845 - 382 pages
...must be the centre. t Dr. Slmson's enunciation is as follows :— " If two circles touch each other internally, the straight line which joins their centres,...produced, shall pass through the point of contact." This is liable to two objections. The circles do not "touch each other internally," the interior one...
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