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 215
SOLID figures contained by the same number of equal Ste N. and similar planes
alike fituated , and having none of their folid angles contained by more than three
plane angles ; are equal and similar to one another . Let AG , KQ be two solid ...
SOLID figures contained by the same number of equal Ste N. and similar planes
alike fituated , and having none of their folid angles contained by more than three
plane angles ; are equal and similar to one another . Let AG , KQ be two solid ...
Page 218
Book XI . multiple soever the base LF is of the base AF , the same multiple is
mthe folid LV of the folid AV . for the same reafon , whatever mul , tiple the base
NF is of the base HF , the same multiple is the solid NV of the solid ED . and if the
...
Book XI . multiple soever the base LF is of the base AF , the same multiple is
mthe folid LV of the folid AV . for the same reafon , whatever mul , tiple the base
NF is of the base HF , the same multiple is the solid NV of the solid ED . and if the
...
Page 220
Book XI . line a solid angle has been made equal to a given solid angle
conWtained by three plane angles . Which was to be done . PROP . XXVII . PROB
. O describe from a given straight line a solid parallelepiped similar , and similarly
...
Book XI . line a solid angle has been made equal to a given solid angle
conWtained by three plane angles . Which was to be done . PROP . XXVII . PROB
. O describe from a given straight line a solid parallelepiped similar , and similarly
...
Page 229
25.11 . and as PE to KM , so d is the solid PL to the folid KO . and therefore as the
solid AB to the solid EX , so is EX to PL , and PL to KO . but if four magnitudes be
continual proportionals , the first is said to have to the fourth the triplicate ratio of ...
25.11 . and as PE to KM , so d is the solid PL to the folid KO . and therefore as the
solid AB to the solid EX , so is EX to PL , and PL to KO . but if four magnitudes be
continual proportionals , the first is said to have to the fourth the triplicate ratio of ...
Page 232
Book XI . therefore the solid AB is to the solid CV , as a the solid CD to the solid
CV . but as the solid AB to the solid CV , so b is the base EH to the base NP ; for
the folds AB , CV are of the same altitude ; and b . 32.11 . as the solid CD to CV ...
Book XI . therefore the solid AB is to the solid CV , as a the solid CD to the solid
CV . but as the solid AB to the solid CV , so b is the base EH to the base NP ; for
the folds AB , CV are of the same altitude ; and b . 32.11 . as the solid CD to CV ...
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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 |