## First Steps in Geometry: A Series of Hints for the Solution of Geometrical Problems with Notes on Euclid, Useful Working Propositions and Many Examples |

### From inside the book

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Page 70

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**AC**in these points respectively , since the angles at M and N are right angles . NOTE . Of course there is no ...**rectangle**under RD , R P ; whence N is given , and the required circle , pass- ing through the three known points , P ... Page 120

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**rectangle**AB ,**A C**, shall be equal to the square on A B. A A ' C B B ' Let A'B ' be equal to A B. Then by Prop . 1 , Rect .**A C**, A'B ' + rect . B C , A ' B ' = rect . A B , A'B ' ; that is , rect .**A C**, A B + rect . BC , AB = sq ... Page 122

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**rectangle**A B , BC together with the square on A C.**A C**1 B By IV . , Sq . on A B = sq . on**AC**+ sq . on BC + 2 rect .**A C**, CB .. sqs . on AB , BC sq . on**AC**+ 2 sq . on BC +2 rect .**A C**, CB = sq . on**AC**+ 2 rect . AB , BC ( by III ... Page 124

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**rectangle**by the whole and one part shall be equal to the square on the other . Bisect A B in C , and from A draw A D perpen- dicular to A B , and**AC**...**rectangle**A B , A F , be equal to the square on B F. A F C FIG . 77 . For sq . on ... Page 125

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**A C**with twice the**rectangle**BD , B C. A A B D FIG . 79 . B FIG . 80 . First , let D fall between B and C ( Fig . 79. ) . Then , sq . on A B and sq . on BC = sq . on A D + sq . on BD = sq . on DC + sq . on BD + 2 rect . BD , DC ...### Other editions - View all

First Steps in Geometry: A Series of Hints for the Solution of Geometrical ... Richard Anthony Proctor No preview available - 2018 |

First Steps in Geometry: A Series of Hints for the Solution of Geometrical ... Richard Anthony Proctor No preview available - 2013 |

### Common terms and phrases

A B C D A B is equal ABCD angle ABC angle BA angle equal base bisector bisects the angle circle diagonals equal and parallel equal angles equal sides equal to DC equal to half equal to twice Euclid exterior angles given angle given line given point given straight line greater Hence hypotenuse intersect isosceles triangle KHGE lines bisecting lines drawn locus maxima and minima obtuse opposite sides parallelogram perpendicular point F problem produced proof Prop proposition quadrilateral R. A. PROCTOR rect rectangle A C rectangle contained respects Euc rhombus right angles right-angled triangle sides A B solution square on CD squares on A C straight line A B theorems trapezium triangle ABC twice the rectangle vertex vertical angle

### Popular passages

Page 80 - If two triangles have two sides of the one equal to two sides of the...

Page 144 - To draw a straight line at right angles to a given straight line, from a given point in the same.

Page 175 - IF a straight line be divided into two equal, and also into two unequal parts ; the squares of the two unequal parts are together double of the square of half the line, and of the square of the line between the points of section.

Page 136 - AB into two parts, so that the rectangle contained by the whole line and one of the parts, shall be equal to the square on the other part.