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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Page 33
XXXVI . Book I. PARALLELOGRAMS upon equal bases and between the same
parallels , are equal to one another . Let ABCD , EFGH be parallelograms upon
equal bases BC , FG , and between the same A D E H parallels AH , BG ; the ...
XXXVI . Book I. PARALLELOGRAMS upon equal bases and between the same
parallels , are equal to one another . Let ABCD , EFGH be parallelograms upon
equal bases BC , FG , and between the same A D E H parallels AH , BG ; the ...
Page 117
F the first be the same multiple of the second , which the third is of the fourth ; and
if of the first and third there be taken equimultiples , these shall be equimultiples
the one of the second , and the other of the fourth . Let A the first be the same ...
F the first be the same multiple of the second , which the third is of the fourth ; and
if of the first and third there be taken equimultiples , these shall be equimultiples
the one of the second , and the other of the fourth . Let A the first be the same ...
Page 119
the first and third have the same ratio to the second and fourth . and Book v . in
like manner the first and the third have the same ratio to any equimultiples
whatever of the second and fourth . Let A the first have to B the second , the fame
ratio ...
the first and third have the same ratio to the second and fourth . and Book v . in
like manner the first and the third have the same ratio to any equimultiples
whatever of the second and fourth . Let A the first have to B the second , the fame
ratio ...
Page 120
Book V. multiple of CF , that AB is of CD ; therefore EB is the same mulwtiple of
FD , that AB is of CD . Therefore if one magnitude , & c . Q.E.D. PROP . VI .
THEOR . F two magnitudes be equimultiples of two others , and See N. if
equimultiples ...
Book V. multiple of CF , that AB is of CD ; therefore EB is the same mulwtiple of
FD , that AB is of CD . Therefore if one magnitude , & c . Q.E.D. PROP . VI .
THEOR . F two magnitudes be equimultiples of two others , and See N. if
equimultiples ...
Page 123
If the first be to the second as the third to the fourth , See N. and if the first be a
multiple , or part of the second ; the third is the same multiple , or the same part of
the fourth . b . A. S. Let A bc to B , as C is to D ; and first let A be a multiple of B ; C
...
If the first be to the second as the third to the fourth , See N. and if the first be a
multiple , or part of the second ; the third is the same multiple , or the same part of
the fourth . b . A. S. Let A bc to B , as C is to D ; and first let A be a multiple of B ; C
...
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Common terms and phrases
added alſo altitude angle ABC angle BAC baſe BC is given becauſe Book Book XI caſe circle circle ABCD circumference common cone 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 AC 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 |