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 .
Seite 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 ...
Seite 32
... 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 whole , or the remainder DF ; AB also is equal to DC ...
... 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 whole , or the remainder DF ; AB also is equal to DC ...
Seite 33
... the like reason the parallelogram EFGH is equal to the same EBCH . therefore also the parallelogram ABCD is equal to EFGH . Wherefore parallelograms , & c . Q. E. D. & G2 TR PROP . XXXVII . THEOR . RIANGLÈS upon the same base ...
... the like reason the parallelogram EFGH is equal to the same EBCH . therefore also the parallelogram ABCD is equal to EFGH . Wherefore parallelograms , & c . Q. E. D. & G2 TR PROP . XXXVII . THEOR . RIANGLÈS upon the same base ...
Seite 37
... the triangle ABC is equal a 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 to the triangle ...
... the triangle ABC is equal a 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 to the triangle ...
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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
Beliebte Passagen
Seite 5 - Let it be granted that a straight line may be drawn from any one point to any other point.
Seite 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.
Seite 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.
Seite 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...
Seite 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...
Seite 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.
Seite 167 - Similar triangles are to one another in the duplicate ratio of their homologous sides.
Seite 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.
Seite 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.
Seite 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.
Bibliografische Informationen
| Titel | 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 ... |
| Autor/in | Robert Simson |
| Verlag | R. and A. Foulis, 1762 |
| Original von | University of Michigan |
| Digitalisiert | 11. Juni 2007 |
| Länge | 466 Seiten |
| Zitat exportieren | BiBTeX EndNote RefMan |