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" Straight lines which are parallel to the same straight line are parallel to one another. Triangles and Rectilinear Figures. The sum of the angles of a triangle is equal to two right angles. "
Elements of Geometry: Containing the First Six Books of Euclid, with a ... - Σελίδα 27
των Euclid, John Playfair - 1853 - 317 σελίδες
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Pantologia. A new (cabinet) cyclopædia, by J.M. Good, O. Gregory ..., Τόμος 5

John Mason Good - 1813
...same side; and likewise the two interior angles upon the same side together equal to two right ansies. Prop. XXX. Theor. Straight lines which are parallel to the same straight line are paiallel to one another. Prop. XXXI. Prob. To draw a straight line thruu0h a given point parallel to...

The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1814
...right angles; therefore also BGH, GHD are equal to two right angles. Wherefore, if a straight, &c. QED PROP. XXX. THEOR. STRAIGHT lines which are parallel to the same straight line are parallel to each other. ' Let the straight line GHK cut AB, EF, CD; and because GHK cuts the parallel / straight...

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

Euclides - 1816 - 528 σελίδες
...right angles ; therefore also BGH, GHD are equal to two right angles. Wherefore, if a straight, &c. QED PROP. XXX. THEOR. STRAIGHT lines which are parallel to the same straight line are parallel to each other. Let AB, CD be each of them parallel to EF ; AB is also parallel to CD. Let the straight...

A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - 1825 - 372 σελίδες
...BGH, GH D are equal to two right angles. Wherefore, if a straight, &c. QED Proposition XXX. Theorem. Straight lines which are parallel to the same straight line are parallel to one another. Lei AB, CD be each of them parallel to EF j AB a alto parallel to CD. Let the straight line GHK cut...

Elements of Arithmetic, Algebra, and Geometry

George Lees - 1826
...parallel, and since they do not meet towards L and D, they must meet if produced towards K and C. Cor. 2. Straight lines which are parallel to the same straight line, are parallel to one another. Scholium. This proposition suggests an 'easy method of drawing a parallel to a given straight line...

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

Robert Simson - 1827 - 513 σελίδες
...therefore also BGH, GHD are equal f to two right angles. Wherefore, if a straight line, &c. Q. £. D. PROP. XXX. THEOR. Straight lines which are parallel to the same straight line are parallel to each other. Let AB, CD be each of them parallel to EF: AB shall be parallel to CD. Let the straight...

Elements of geometry: Being chiefly a selection from Playfair's geometry

John Playfair - 1829 - 186 σελίδες
...the cutting line, and the sum of the two interior angles on the same side equal to two right angles. Straight lines which are parallel to the same straight line are parallel to one another. Mutual Equality of Triangles. When the three sides of one triangle are respectively equal to the three...

Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - 1830 - 272 σελίδες
...С : the straight lines pq, p' q1 produced, shall, each of them, pass through the point C. Because straight lines which are parallel to the same straight line are parallel to one another (IV. 6.) VC, which is parallel to PQ, is parallel also to P'Q'. But it has been already shown (2 Cor....

The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1834
...BGH, GHD are equal f to two right angles. Wherefore, if afl Ax. straight line., &c. QED PROPOSITION XXX. THEOR. — Straight lines which are parallel to the same straight line, are parallel to each other. Let AB, CD be each of them parallel to EF: AB shall be parallel to CD. Let the straight...

Library of Useful Knowledge: Geometry, plane, solid, and spherical [by ...

1835
...in С : the straight lines pq, p'q produced, shall, each of them, pass through the point C. Because straight lines which are parallel to the same straight line are parallel to one another (IV. 6.) VC, which is parallel to PQ, is parallel also to P'Q'. But it has been already shown (2 Cor....




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