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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Resultat 1-5 av 14
Side 40
From the point A draw a AC at right angles to AB ; and make b AD equal to AB ,
and thro ' the point D draw DE parallel to it , f . 31. d , and thro ' B draw BE parallel
to AD , therefore ADEB is a paralled . 34. 1. logram ; whence AB is equal to DE ...
From the point A draw a AC at right angles to AB ; and make b AD equal to AB ,
and thro ' the point D draw DE parallel to it , f . 31. d , and thro ' B draw BE parallel
to AD , therefore ADEB is a paralled . 34. 1. logram ; whence AB is equal to DE ...
Side 41
then because each of the angles BAC , BAG is a right angle " , the two straight
lines b . 31.1 . AC , AG upon the opposite G fides of AB , make with it at H the
point A the adjacent angles ecual to two right angles ; therefore CA is in the same
K ...
then because each of the angles BAC , BAG is a right angle " , the two straight
lines b . 31.1 . AC , AG upon the opposite G fides of AB , make with it at H the
point A the adjacent angles ecual to two right angles ; therefore CA is in the same
K ...
Side 85
THEOR . a circle , the angle in a semicircle is a right angle ; but the angle in a
segment greater than a semicircle is less than a right angle ; and the angle in a
segment less than a semicircle is greater than a right angle . Let ABCD be a
circle ...
THEOR . a circle , the angle in a semicircle is a right angle ; but the angle in a
segment greater than a semicircle is less than a right angle ; and the angle in a
segment less than a semicircle is greater than a right angle . Let ABCD be a
circle ...
Side 194
AB , BC . and because AB stands at right angles to each of the b.4 . 11. straight
lines BD , BE , it is also at right angles b to the plane passing through them ; and
therefore makes c.3.Def . 11. right angles « with every straight line A meeting it in
...
AB , BC . and because AB stands at right angles to each of the b.4 . 11. straight
lines BD , BE , it is also at right angles b to the plane passing through them ; and
therefore makes c.3.Def . 11. right angles « with every straight line A meeting it in
...
Side 196
Let AB , CD be two parallel straight lines , and let one of the AB be at right angles
to a plane ; the other CD is at right angles to the same plane . Let AB , CD meet
the plane in the points B , D , and join BD . therefore AB , CD , BD are in one ...
Let AB , CD be two parallel straight lines , and let one of the AB be at right angles
to a plane ; the other CD is at right angles to the same plane . Let AB , CD meet
the plane in the points B , D , and join BD . therefore AB , CD , BD are in one ...
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The Elements of Euclid, Viz: The Errors, by which Theon, Or Others, Have ... Robert Simson Uten tilgangsbegrensning - 1775 |
The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ... Robert Simson Uten tilgangsbegrensning - 1827 |
The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ... Robert Simson Uten tilgangsbegrensning - 1781 |
Vanlige uttrykk og setninger
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
Populære avsnitt
Side 5 - Let it be granted that a straight line may be drawn from any one point to any other point.
Side 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.
Side 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.
Side 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...
Side 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...
Side 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.
Side 167 - Similar triangles are to one another in the duplicate ratio of their homologous sides.
Side 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.
Side 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.
Side 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.
Bibliografisk informasjon
| Tittel | 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 ... |
| Forfatter | Robert Simson |
| Utgiver | R. and A. Foulis, 1762 |
| Original fra | University of Michigan |
| Digitalisert | 11. jun 2007 |
| Lengde | 466 sider |
| Eksporter sitat | BiBTeX EndNote RefMan |