The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected and Some of Euclid's Demonstrations are Restored. Also, to this Second Edition is Added the Book of Euclid's Data. In Like Manner Corrected. viz. the first six books, together with the eleventh and twelfth |
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... which are not similar unto one another , in the true sense of similarity received by all Geometers . and all these Propositions have , for these reasons , been infufficiently demonstrated since Theon's time hitherto .
... which are not similar unto one another , in the true sense of similarity received by all Geometers . and all these Propositions have , for these reasons , been infufficiently demonstrated since Theon's time hitherto .
Page 21
Again because the exterior angle of a triangle is greater than the interior and opposite angle , the exterior angle BDC of the triangle CDE is greater than CED . for the same reason , the exterior angle CEB of the triangle ABE is ...
Again because the exterior angle of a triangle is greater than the interior and opposite angle , the exterior angle BDC of the triangle CDE is greater than CED . for the same reason , the exterior angle CEB of the triangle ABE is ...
Page 32
... then because ABCD is a parallelogram , AD is equal BC ; for the same reason , EF is equal to BC ; wherefore AD is 6. 1. Ax . equal 6 to EF ; and DE is common ; therefore the whole , or the c . 2. or 3. remainder , AE is equal to the ...
... then because ABCD is a parallelogram , AD is equal BC ; for the same reason , EF is equal to BC ; wherefore AD is 6. 1. Ax . equal 6 to EF ; and DE is common ; therefore the whole , or the c . 2. or 3. remainder , AE is equal to the ...
Page 33
6. 33. to fore EB , CH are both equal and parallel , and EBCH is a parallelogram ; and it is equal to ABCD , because it is upon the same base c . 15. to BC , and between the fame parallels BC , AD . for the like reason ...
6. 33. to fore EB , CH are both equal and parallel , and EBCH is a parallelogram ; and it is equal to ABCD , because it is upon the same base c . 15. to BC , and between the fame parallels BC , AD . for the like reason ...
Page 37
... and AC its diameter , the triangle ABC is equal to the triangle ADC . and because EKHA is a parallelogram , the diameter of which is AK , the triangle AEK is equal to the triangle AHK , by the same reason , the triangle KGC is equal ...
... and AC its diameter , the triangle ABC is equal to the triangle ADC . and because EKHA is a parallelogram , the diameter of which is AK , the triangle AEK is equal to the triangle AHK , by the same reason , the triangle KGC is equal ...
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added alſo altitude angle ABC angle BAC baſe BC is given becauſe Book caſe circle circle ABCD circumference common cone contained cylinder Definition demonſtrated deſcribed diameter divided double draw drawn equal equal angles equiangular equimultiples exceſs fame fides firſt folid fore four fourth given angle given in poſition given in ſpecies given magnitude given ratio given ſtraight line greater Greek half join leſs likewiſe magnitude manner meet muſt oppoſite parallel parallelogram perpendicular plane priſm produced PROP proportionals Propoſition pyramid reaſon rectangle remaining right angles ſame ſecond ſegment ſhall ſhewn ſides ſimilar ſolid ſquare ſquare of BC taken THEOR theſe third thro triangle ABC wherefore whole
Popular passages
Page 5 - Let it be granted that a straight line may be drawn from any one point to any other point.
Page 163 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Page 48 - If a straight line be divided into any two parts, the squares of the whole line, and of one of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into any two parts in the point C; the squares of AB, BC are equal to twice the rectangle AB, BC, together with the square of AC.
Page 73 - The straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle; and no straight line can be drawn from the extremity between that straight line and the circumference, so as not to cut the circle...
Page 105 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...
Page 3 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.
Page 167 - Similar triangles are to one another in the duplicate ratio of their homologous sides.
Page 54 - AB be the given straight line ; it is required to divide it into two parts, so that the rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part.
Page 47 - If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line.
Page 37 - To describe a parallelogram that shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Bibliographic information
| Title | The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected and Some of Euclid's Demonstrations are Restored. Also, to this Second Edition is Added the Book of Euclid's Data. In Like Manner Corrected. viz. the first six books, together with ... |
| Author | Robert Simson |
| Publisher | R. and A. Foulis, 1762 |
| Original from | the University of Michigan |
| Digitized | 11 Jun 2007 |
| Length | 466 pages |
| Export Citation | BiBTeX EndNote RefMan |