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" ... than the more remote: but of those which fall upon the convex circumference, the least is that between the point without the circle and the diameter; and, of the rest, that which is nearer to the least is always less than the more remote: and only... "
The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... - Σελίδα 64
των Euclid - 1835 - 513 σελίδες
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Elements of geometry, based on Euclid, books i-iii

Edward Atkins - 1876 - 119 σελίδες
...one passing through the centre is always greater than one more remote ; but of those which fall on the convex circumference, the least is that between...point without the circle and the diameter; and of t\o rest, that which is nearer in the least is always less than one more remote ; and from the same...

The Elements of Euclid for the Use of Schools and Colleges: With Notes, an ...

Isaac Todhunter - 1880 - 400 σελίδες
...greater than one more remote; but of those which fall on the convex circumference, the least is tliat between the point without the circle and the diameter;...that which is nearer to the least is always less than one more remote ; and from the same point there can be drawn to the circumference two straight lines,...

The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - 1883 - 400 σελίδες
...the centre is always greater than one more remote; but of those which fall on the EUCLID'S ELEMENTS. convex circumference, the least is that between the...that which is nearer to the least is always less than one more remote ; and from the same point there can be drawn to the circumference t^co straight lines,...

Knowledge: An Illustrated Magazine of Science, Τόμος 5

1884
...a given point to a given straight line ; and of others that which is nearer to the perpendicular is less than the more remote ; and only two equal straight lines can be drawn from the piven point to the given straight line, one on each side of the perpendicular. 53. P and Q are points...

First Steps in Geometry: A Series of Hints for the Solution of Geometrical ...

Richard Anthony Proctor - 1887 - 180 σελίδες
...a given point to a given straight line ; and of others that which is nearer to the perpendicular is less than the more remote ; and only two equal straight lines can be drawn from the given point to the given straight line, one on each side of the perpendicular. 53. P and Q are points...

Woolwich Mathematical Papers for Admission Into the Royal Military Academy ...

E. J. Brooksmith - 1889
...one passing through the centre is always greater than one more remote ; but of those which fall on the convex circumference, the least is that between...that which is nearer to the least is always less than one more remote. Prove that the two lines which are equally inclined to the shortest line are equal....

The Harpur Euclid: An Edition of Euclid's Elements

Edward Mann Langley, W. Seys Phillips - 1890 - 515 σελίδες
...nearer to the one through the centre is always greater than one more remote. (2) Of those which fall on the convex circumference, the least is that between...that which is nearer to the least is always less than one more remote. (3) From the same point there can be drawn to the circumference two straight lines,...

Books 3-9

Euclid - 1908
...on the convex circumference, that between the point and the diameter is least, while of the rest the nearer to the least .is always less than the more remote, and only two equal straight lines will fall on the circle from the point, one on each side of the least. Let ABC be a circle, and let...

The Scientific Letters and Papers of James Clerk Maxwell: Volume 1, 1846-1862

James Clerk Maxwell - 1990 - 776 σελίδες
...is nearer to that through the centre is always greater than the more remote: But of those which fall upon the convex circumference, the least is that between...the circumference, one upon each side of the least' (Elements: 77). Proposition 8 - Theorem If a line AE be cut in C and B, so that AB:BC::AE:CE, and two...
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Apollonius of Perga's Conica: Text, Context, Subtext

Michael N. Fried - 2001 - 499 σελίδες
...on the convex circumference, that between the point and the diameter is least, while of the rest the nearer to the least is always less than the more remote, and only two equal straight lines will fall on the circle from the point, one on each side of the least." So, DA passing through the...
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