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" Let it be granted that a straight line may be drawn from any one point to any other point. "
Elements of Geometry: On the Basis of Dr. Brewster's Legendre : to which is ... - Page 220
by James Bates Thomson - 1844 - 237 pages
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Gradations in Euclid : books i. and ii., with an explanatory preface [&c ...

Euclides - 1858 - 248 pages
...between the same parallels, the parallelogram shall be double of the triangle. CONSTRUCTION. — Pst. 1. A straight line may be drawn from any one point to any other point. DEMONSTRATION. — P. 37. Triangles upon the same base and between the same parallels, are equal to...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - Geometry, Plane - 1860 - 380 pages
...diagonal is the straight line joining two of its opposite angles. POSTULATES. I. LET it be granted that a straight line may be drawn from any one point to any other point. n. That a terminated straight line may be produced to any length in a straight line. in. And that a...
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The Intuitions of the Mind Inductively Investigated

James McCosh - History - 1860 - 512 pages
...definitions and in the propositions founded on them, such as the following, put in the form of maxims:—" A straight line may be drawn from any one point to any other point;" "A straight line may be produced to any length in a straight line;" "There may be such a figure as...
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Euclid's plane geometry, books iii.-vi., practically applied; or, Gradations ...

Euclides - 1861 - 464 pages
...PROP. 1. — PROK. To find the centre of a given circle. SOL. — Pst. 1. Let it be granted that a st. line may be drawn from any one point to any other point. 10, I. To bisect a given finite st. line. 11, I. To draw a st. line at rt.¿s to a given st. line from...
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The school Euclid: comprising the first four books, by A.K. Isbister

Euclides - 1862 - 172 pages
...plane, and which being produced ever so far both ways do not meet. POSTULATES. I. Let it be granted that a straight line may be drawn from any one point to any other point. II. That a terminated straight line may be produced to any length in a straight line. III. AXIOMS....
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The elements of plane geometry; or, The first six books of Euclid, ed. by W ...

Euclides - 1863 - 122 pages
...That a terminated straight line may be produced to any length in a straight line. 1. Let it be granted that a straight line may be drawn from any one point to any other point. 3. And that a circle may be described from any centre, at any distance from that centre. AXIOMS. 1....
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The school edition. Euclid's Elements of geometry, the first six books, by R ...

Euclides - 1864 - 448 pages
...diagonal is the straight line joining two of its opposite angles. POSTULATES. I. LET it be granted that a straight line may be drawn from any one point to any other point. II. That a terminated straight line may be produced to any length in a straight line. m. And that a...
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Elements of plane geometry, book i, containing nearly the same propositions ...

Euclides - 1865 - 80 pages
...expression for drawing a straight line from the one of them to the other. POSTULATES. 1. Let it be granted that a straight line may be drawn from any one point to any other point. 2. That a straight line may be produced in a straight line to any required length. 3. That a circle may be described...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson ...

Robert Potts - 1865 - 528 pages
...a diagonal is a straight linn joining two of its opposite angles. POSTULATES. I. LET it be granted, that a straight line may be drawn from any one point to any other point. n. That a terminated straight line may be produced to any length in a straight line. m. And that a...
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The College Euclid: Comprising the First Six and the Parts of the Eleventh ...

Euclides - 1865 - 402 pages
...plane, and which being prodnced ever so far both ways do not meet. POSTULATES. L Let it be granted that a straight line may be drawn from any one point to any other point. IL That a terminated straight line may be prodnced to any length in a straight line. HI. And that a...
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