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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Seite 10
In BD take any point F , and from AE , the greater , cut off AG equal to AF , the less , and join FC , GB . Because AF is equal to AG , and AB to AC ; the two sides FA , AC are equal to the two GA , AB , each to each ; and they contain ...
In BD take any point F , and from AE , the greater , cut off AG equal to AF , the less , and join FC , GB . Because AF is equal to AG , and AB to AC ; the two sides FA , AC are equal to the two GA , AB , each to each ; and they contain ...
Seite 11
2.1 . less , and join DC , therefore because in the A triangles DBC , ACB , DB is equal to AC , and BC common to both , the two sides D DB , BC are equal to the two AC , CB , each to each ; and the angle DBC is equal to the angle ACB ...
2.1 . less , and join DC , therefore because in the A triangles DBC , ACB , DB is equal to AC , and BC common to both , the two sides D DB , BC are equal to the two AC , CB , each to each ; and the angle DBC is equal to the angle ACB ...
Seite 13
AD ; join DE , and upon it defcribeban b . 1. 1 . А equilateral triangle DEF , then join AF . the straight line AF bisects the angle BAC . Because AD is equal to AE , and AF D E is common to the two triangles DAF , EAF ; the two sides ...
AD ; join DE , and upon it defcribeban b . 1. 1 . А equilateral triangle DEF , then join AF . the straight line AF bisects the angle BAC . Because AD is equal to AE , and AF D E is common to the two triangles DAF , EAF ; the two sides ...
Seite 14
... and join FC . the straight line FC drawn from the given point C , is at right angles to the given straight line AB . Because DC is equal to CE , and FC cominon to the two tri- A С angles DCF , ECF ; the two sides DC , CF are equal ...
... and join FC . the straight line FC drawn from the given point C , is at right angles to the given straight line AB . Because DC is equal to CE , and FC cominon to the two tri- A С angles DCF , ECF ; the two sides DC , CF are equal ...
Seite 18
Bisect a AC in E , join BE A and produce it to F , and make EF equal to BE ; join also FC , and produce AC to G. Because AE is equal to ÈC , and BE to EF ; AE , EB are equal to CE , EF , each to each ; and the angle AEB B C b . 15.
Bisect a AC in E , join BE A and produce it to F , and make EF equal to BE ; join also FC , and produce AC to G. Because AE is equal to ÈC , and BE to EF ; AE , EB are equal to CE , EF , each to each ; and the angle AEB B C b . 15.
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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 |