Elements of plane geometry, book i, containing nearly the same propositions as the first book of Euclid's Elements |
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Seite 3
... SAME PROPOSITIONS AS THE FIRST BOOK OF EUCLID'S ELEMENTS : IN WHICH AN ATTEMPT IS MADE TO IMPROVE THE ARRANGEMENT AND SUPPLY THE DEFECTS OF THAT BOOK , AND ALSO TO GIVE A DIRECT DEMONSTRATION OF THE PROPERTIES OF PARALLEL LINES .
... SAME PROPOSITIONS AS THE FIRST BOOK OF EUCLID'S ELEMENTS : IN WHICH AN ATTEMPT IS MADE TO IMPROVE THE ARRANGEMENT AND SUPPLY THE DEFECTS OF THAT BOOK , AND ALSO TO GIVE A DIRECT DEMONSTRATION OF THE PROPERTIES OF PARALLEL LINES .
Seite 16
No part of elementary geometry since the time of Euclid has - caused so much perplexity and annoyance to geometers as the subject of parallel lines . There is no great difficulty in demonstrating , that if two straight lines make equal ...
No part of elementary geometry since the time of Euclid has - caused so much perplexity and annoyance to geometers as the subject of parallel lines . There is no great difficulty in demonstrating , that if two straight lines make equal ...
Seite 17
at first to demonstrate the properties of parallel lines by the aid of the truths which he had already established , but , finding these insufficient , he was under the necessity of assuming an additional principle in order to effect ...
at first to demonstrate the properties of parallel lines by the aid of the truths which he had already established , but , finding these insufficient , he was under the necessity of assuming an additional principle in order to effect ...
Seite 18
By the method of supraposition , this proposition cannot be established until the properties of parallel lines have been demonstrated , and this cannot be effected without the assumption of some additional principle equivalent to ...
By the method of supraposition , this proposition cannot be established until the properties of parallel lines have been demonstrated , and this cannot be effected without the assumption of some additional principle equivalent to ...
Seite 20
Then , by means of the definition of parallel lines here adopted , the proof that lines equally inclined to one line must be so to every other line , follows directly from the proposition already stated ...
Then , by means of the definition of parallel lines here adopted , the proof that lines equally inclined to one line must be so to every other line , follows directly from the proposition already stated ...
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Elements of Plane Geometry, Book: Containing Nearly the Same Propositions As ... Euclid Keine Leseprobe verfügbar - 2008 |
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ABC is equal AC is equal acute adjacent alternate angles ancient angle ACD angle BAC angles ABC appears application assume axiom base BC bisect called centre circle circumference coincide common conclusion construction definition demonstration describe determined diagonal draw drawn elements employed established Euclid extended exterior angle extremities fall four right angles geometers geometry given straight line greater half Hence included angle interior opposite angle intersect introduced join knowledge less Let ABC magnitudes manner means meet method mind mode necessary obtuse parallel lines parallelogram perpendicular plane position principle problem produced proof properties PROPOSITION proved radiant reason rectangle rectilineal figure remaining respects side AB side AC surfaces THEOR thing third triangle ABC triangles are equal truths unequal vertex wherefore whole
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Seite 43 - If two triangles have two sides and the included angle of the one, equal to two sides and the included angle of the other, each to each, the two triangles will be equal.
Seite 46 - Any two angles of a triangle are together less than two right angles.
Seite 37 - The angles which one straight line makes with another upon one tide of it, are either two right angles, or are together equal to two right angles. Let the straight line AB make with CD, upon one side of it the angles CBA, ABD ; these are either two right angles, or are together equal to two right angles. For, if the angle CBA be equal to ABD, each of them is a right angle (Def.
Seite 57 - Through a given point to draw a straight line parallel to a given straight line, Let A be the given point, and BC the given straight line : it is required to draw through the point A a straight line parallel to BC.
Seite 38 - ... in one and the same straight line. At the point B in the straight line AB, let the two straight lines BC, BD upon the opposite sides of AB, make the adjacent angles ABC, ABD, equal together to two right angles. BD is in the same straight line with CB.
Seite 68 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Seite 34 - LET it be granted that a straight line may be drawn from any one point to any other point.
Seite 64 - Parallelograms upon the same base, and between the same parallels, are equal to one another.
Seite 46 - If one side of a triangle be produced, the exterior angle is greater than either of the interior, and opposite angles.
Seite 34 - Things which are equal to the same thing are also equal to one another. 2. If equals be added to equals, the wholes are equal. 3. If equals be subtracted from equals, the remainders are equal.