## 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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**Prop**. 19 , Bk . I. It naturally occurs to us , therefore , to apply this proposition . We have to show that DC is greater than BC , and we know from Euc . I. , 19 , that if DC is greater than B C , then the angle DBC is greater than ... Page 20

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**Props**. 10-12 . It should be included amongst the additional problems a knowledge of which is neces- sary to those who wish to work successfully at deductions . DF being equal to DC , we may be led 20 GEOMETRICAL PROBLEMS . Page 24

... are severally double of A B. 2 In constructing the figure , proceed thus : -Take A D equal to A E , and join D E ; then take P , a point dividing D E into unequal parts .

... are severally double of A B. 2 In constructing the figure , proceed thus : -Take A D equal to A E , and join D E ; then take P , a point dividing D E into unequal parts .

**Prop**. 5. This gives us the angle A D 24 GEOMETRICAL PROBLEMS . Page 25

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**Prop**. 5. This gives us the angle A D E equal to the angle A E D — a property which avails us nothing . But there are other properties of isosceles tri- angles , not expressly mentioned by Euclid , with which every geometrician ought to ... Page 38

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**Prop**. 4 and elsewhere ) assumed the property as self - evident , and that**Prop**. 12 itself cannot be solved on any other assumption . conceive the part of the figure to the right of 38 GEOMETRICAL PROBLEMS .### 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.