## 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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**perpendicular**to it . [ That there may be two such angles equal , may be exhi- bited by the following figures : D B C B C B DC meets the right line ACB , and makes two angles DCB and DCA . Suppose DC to be moveable round the fixed point ... Page 31

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**perpendicular**to AB from the point C. Take any point D upon the other side of AB , H A F G B D and from the centre C , at the distance CD , a describe the circle EGF meeting AB in FG ; and bisect FG in H , and join CF , CH , CG ; the ... Page 75

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**perpendicular**at the end of a line without producing it , use the following method : Take any point B on the line required . On AB con- struct an equilateral triangle AOB . Produce BO to P cutting off OP equal to OB . PA shall be ... Page 80

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**perpendicular**is the shortest straight line from a given point to a given straight line . Take any other straight line PR , and prove by means of Propositions , I. 32. and I. 19 . P R 2. Through a given point to draw a straight line ... Page 81

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**perpendicular**, and produce it to O , making AO equal to AP . Join OQ . The lines PR , RQ shall be those required . Prove by I. 4. , the angle PRA Р A R. B equal to the angle ORA , and equal to QRB by means of I. 15 . G BOOK I. 7. In ...### 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.