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
... than three plane angles ; for , in other cases , two folid figures may be
contained by similar planes of the fame number and magnitude , and yet be
unequal to one another ; as thall be made evident in the No : es fubjoined to
these Elements .
... than three plane angles ; for , in other cases , two folid figures may be
contained by similar planes of the fame number and magnitude , and yet be
unequal to one another ; as thall be made evident in the No : es fubjoined to
these Elements .
Page 41
I. the fame reason , AB and AH ale in the same straight line . and because the
angle DBC is equal to the angle FBA , each of them being a right angle , add to
each the angle ABC , E and the whole angle DBA is equal o to the whole FBC.
I. the fame reason , AB and AH ale in the same straight line . and because the
angle DBC is equal to the angle FBA , each of them being a right angle , add to
each the angle ABC , E and the whole angle DBA is equal o to the whole FBC.
Page 264
... is greater than E G the third part of the cylinder , but this pyramid is the third
part of the pri in upon the fame base AEBFCGDH , B and of the fame altitude with
the cyF linder , therefore this prism is greater than the cylinder of which the base
is ...
... is greater than E G the third part of the cylinder , but this pyramid is the third
part of the pri in upon the fame base AEBFCGDH , B and of the fame altitude with
the cyF linder , therefore this prism is greater than the cylinder of which the base
is ...
Page 310
In Like Manner Corrected. viz. the first six books, Robert Simson. Book v . in this
case likewise AB is to CD , as EF to GH . Let CK be a part of CD , and GL the
fame part of GH ; and let AR bc the fame multiple of CK , that EF is of GL .
therefore by ...
In Like Manner Corrected. viz. the first six books, Robert Simson. Book v . in this
case likewise AB is to CD , as EF to GH . Let CK be a part of CD , and GL the
fame part of GH ; and let AR bc the fame multiple of CK , that EF is of GL .
therefore by ...
Page 335
their bafes the fame straight lines AB , BC , CA , now the three Book XI . triangles
GAB , GBC , GCA are common to both folids , and the three others EAB , EBC ,
ECA of the first solid have been mewn equal and similar to the three others FAB ...
their bafes the fame straight lines AB , BC , CA , now the three Book XI . triangles
GAB , GBC , GCA are common to both folids , and the three others EAB , EBC ,
ECA of the first solid have been mewn equal and similar to the three others FAB ...
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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 |