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 |
From inside the book
Results 1-5 of 5
Page 8
Book I. Because the point B is the center of the circle CGH , BC is equal o to BG .
and because D is the center of the circle GKL , DL is equal ¢ . 15. Def . to DG ,
and DA , DB parts of them are equal ; therefore the remainder f . 3. Ax . AL is
equal ...
Book I. Because the point B is the center of the circle CGH , BC is equal o to BG .
and because D is the center of the circle GKL , DL is equal ¢ . 15. Def . to DG ,
and DA , DB parts of them are equal ; therefore the remainder f . 3. Ax . AL is
equal ...
Page 10
Book I. to AC , and let the straight lines AB , AC be produced to D and E. the
angle ABC shall be equal to the angle ACB , and the angle CBD to the angle
BCE . In BD take any point F , and from AE , the greater , cut off AG equal to AF ,
the less ...
Book I. to AC , and let the straight lines AB , AC be produced to D and E. the
angle ABC shall be equal to the angle ACB , and the angle CBD to the angle
BCE . In BD take any point F , and from AE , the greater , cut off AG equal to AF ,
the less ...
Page 25
equal to DE , and BC to EF , the two sides GB , BC are equal to the Book I. two
DE , EF , each to each ; and the angle GBC is equal to the angle DEF ; therefore
the base GC is equal • to the base DF , and the tri - a . 4. 1 . angle GBC to the ...
equal to DE , and BC to EF , the two sides GB , BC are equal to the Book I. two
DE , EF , each to each ; and the angle GBC is equal to the angle DEF ; therefore
the base GC is equal • to the base DF , and the tri - a . 4. 1 . angle GBC to the ...
Page 219
KH equal to GF , and join AH . then the solid angle at A which is m contained by
the three plane angles BAL , BAH , HAL is equal to C. 19 , 18 . the solid angle at
D contained by the three plane angles EDC , EDF , FDC . Take the equal straight
...
KH equal to GF , and join AH . then the solid angle at A which is m contained by
the three plane angles BAL , BAH , HAL is equal to C. 19 , 18 . the solid angle at
D contained by the three plane angles EDC , EDF , FDC . Take the equal straight
...
Page 236
Def.11 . anglesdwith every straight line meeting it in that plane . but BH meets it in
that plane ; ' therefore ABH is a right angle . for the same reafon , DEM is a right
angle , and is therefore equal to the angle ABH . and the angle HAB is equal to ...
Def.11 . anglesdwith every straight line meeting it in that plane . but BH meets it in
that plane ; ' therefore ABH is a right angle . for the same reafon , DEM is a right
angle , and is therefore equal to the angle ABH . and the angle HAB is equal to ...
What people are saying - Write a review
We haven't found any reviews in the usual places.
Other editions - View all
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 |