## The first two books of the Elements of Euclid, with additional figures, notes, explanations, and deductions, by N. Pocock1852 |

### From inside the book

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**angles**of which the equal sides are**opposite**, shall be equal each to each , B C E viz . the**angle**ABC to the**angle**DEF , and the**angle**ACB to DFE . For , if the triangle ABC be applied to DEF , so that the point A may be on D , and the ... Page 19

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**angles**contained by those sides equal to one another , their bases shall likewise be equal , and the triangles be equal , and their other**angles**to which the equal sides are**opposite**shall be equal , each to each . Which was to be ... Page 20

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**angle**ABC shall be equal to the**angle**ACB , and the**angle**CBD to the**angle**BCE . D A B C E In BD take any point F ...**opposite**; viz . the**angle**ACF to the**angle**ABG , and the**angle**AFC to the**angle**AGB : And because the whole AF ... Page 21

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**angle**CGB , and the base BC is common to the two triangles BFC , CGB ; wherefore the triangles are equalb and their remaining**angles**, each to each , to which the equal sides are**opposite**; F therefore the**angle**FBC is equal to the ... Page 22

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**opposite**to , the equal**angles**, shall be equal to one another . Let ABC be a triangle having the**angle**ABC equal to the**angle**ACB ; the side AB is also equal to the side AC . For , if AB be not equal to AC , one of them is greater ...### Other editions - View all

The First Two Books of the Elements of Euclid, with Additional Figures ... Euclides No preview available - 2016 |

### Common terms and phrases

adjacent angles alternate angles angle ABC angle ACB angle AGH angle BAC angle BCD angle EDF angled triangle angles CBA angles equal Arithmetic base BC BC is equal bisected BOOK bound centre cloth coincide Delectus diameter double English Notes equal to BC equal to twice Eton Eton College Euclid's Elements Exercises exterior angle four right angles Geography given point given rectilineal angle given straight line gnomon greater Greek half a right interior and opposite isosceles JANE MARCET join Let ABC Let the straight Lexicon M.A. New Edition Maps opposite angle parallel to CD parallelogram perpendicular Post 8vo produced Proposition rectangle BC rectangle contained rectilineal figure remaining angle rhombus right angles Schools Shrewsbury School sides BA sides equal square described square of AC THEOR triangle ABC twice the rectangle VALPY Valpy's wherefore xxxi

### Popular passages

Page 18 - If two triangles have two sides of the one equal to two sides of the...

Page 67 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.

Page 51 - That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.

Page 109 - ... subtending the obtuse angle, is greater than the squares of the sides containing the obtuse angle, by twice the rectangle contained by the side upon which, when produced, the perpendicular falls, and the straight line intercepted without the triangle between the perpendicular and the obtuse angle. Let ABC be an obtuse-angled triangle, having the obtuse angle ACB, and from the point A let AD be drawn perpendicular to BC produced.

Page 12 - Mrs. R. Lee's Elements of Natural History ; or, First Principles of Zoology : Comprising the Principles of Classification, interspersed with amusing and instructive Accounts of the most remarkable Animals.

Page 53 - To draw a straight line through a given point parallel to a given straight line. Let A be the given point, and BC the given straight line ; it is required to draw a straight line E iR.

Page 76 - In any right-angled triangle, the square which is described upon the side subtending the right angle, is equal to the squares described upon the sides which contain the right angle.

Page 34 - ABD, the less to the greater, which is impossible ; therefore BE is not in the same straight line with BC. And in like manner, it may be demonstrated, that no other can be in the same straight line with it but BD, which therefore is in the same straight line with CB.

Page 11 - LET it be granted that a straight line may be drawn from any one point to any other point.

Page 37 - Any two angles of a triangle are together less than two right angles. Let ABC be any triangle ; any two of its angles together are less than two right angles.