## Skeleton propositions &c. of Euclid, books i and ii, with references, by H. Green, Volume 21858 |

### From inside the book

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Page 85

... square of the whole line equals the squares of the two parts , together with

... square of the whole line equals the squares of the two parts , together with

**twice the rectangle**contained by the parts . CON . 46. Pst . 1 , 31 I. DEM . 29. I , Def . 30. I , 5. I , Ax . 1. 6. I , Ax . 3. 34. I , 43. I. EXP . 1 Hyp . 2 ... Page 95

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**twice the rectangle**contained by the whole and that part , together with the square of the other part . CON . 46. I , Pst . 1. 31. I , DEM . 43. I , Ax . 2. 6 , Def . 30. I , Cor . 4. II , Ax . 8. 34. I. Exp . 1 Hyp . Concl . CON ... Page 96

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**twice the rectangle**under them together with the square of the difference . COR . 2 . The square of the sum of two lines , the sum of their squares , and the square of their difference , are in arithmetical progression , -- the common ...### Other editions - View all

Skeleton Propositions &c. Of Euclid, Books I And Ii, With References, By H ... Euclides No preview available - 2019 |

Skeleton Propositions &c. Of Euclid, Books I And Ii, With References, By H ... Euclides No preview available - 2019 |

Skeleton Propositions &C. of Euclid, Books I and II, with References, by H ... Euclides No preview available - 2015 |

### Common terms and phrases

21 Recap 9 Ax Algebra and Arithmetic Aly & Arith Area Arith COR bisected and produced BOOKS OF EUCLID Conc Concl Cone Construction and Demonstration consult the Gradations cut a line cut in extreme equal to twice equals the square EXPLANATORY PREFACE extreme and mean GEOMETRICAL REASONING GEOMETRY given rectilineal GRADATIONS IN EUCLID half the line half the square half their difference half their sum Learner Let a line line be bisected line be divided line CF line in extreme line intercepted line thus produced lines is equal mean ratio obtuse angle PEN-AND-INK EXAMINATIONS perp points of section PROP recapitulatory exercise rectangle contained references SECOND BOOKS side A B side subtending SKELETON PROPOSITIONS square of half squares is equal SYNOPSIS BK THEOR triangle truths twice the rect twice the rectangle twice the square unequal whole line

### Popular passages

Page 95 - 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 99 - 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 105 - To divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts, shall be equal to the square on the other part.

Page 93 - If a straight line be bisected, and produced to any point ; the rectangle contained by the whole line thus produced, and the part of it produced, together with the square...

Page 101 - IF a straight line be bisected, and produced to any point, the square of the whole line thus produced, and the square of the part of it produced, are together double of the square of half the line bisected, and of the square of the line made up of the half and the part produced.

Page 81 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line. Let...

Page 107 - IN obtuse angled triangles, if a perpendicular be drawn from any of the acute angles to the opposite side produced, the square of the side 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.

Page 96 - AB2+CK=2AB.BC-fHF, that is, (since CK=CB2, and HF=AC2,) AB2+CB2=2AB.BC+AC2. " COR. Hence, the sum of the squares of any two lines is equal to " twice the rectangle contained by the lines together with the square of