## Elementary Geometry: Practical and Theoretical |

### From inside the book

Page 226

...

...

**LAPB**Data QE falls along PB , and since the circumferences coincide , D coincides with A , and E with B. .. arc DHE coincides with arc AGB . .. arc DHE arc AGB . ( 2 ) CONVERSE PROPOSITION . Data To prove that arc AGB arc DHE . = Ls APB ... Page 227

...

...

**LAPB**. Q. E. D. COR . Equal angles at the centre determine equal sectors . NOTE ON THE CASE OF " THE SAME CIRCLE . " The above proposition is proved for equal circles . To see that it applies to arcs and angles in the same circle , let ... Page 228

...

...

**LAPB**= 4 DQE , == .. arc AGB : = arc DHE , Again , whole circumference of ABC ference of DEF . .. the remaining arc ACB ( 2 ) CONVERSE PROPOSITION . Data To prove that Construction arc AGB = whole circum- = the remaining arc DFE . arc ... Page 229

...

...

**LAPB**4 DQE .. in the As APB , DQE AP = DQ , BP = EQ , △ APB = △ DQE . .. the triangles are congruent , .. chord AB = chord DE . Q. E. D. I. 10 . Ex . 1182. A quadrilateral ABCD is inscribed in a circle , and AB = CD . Prove that AC ... Page 252

...

...

**LAPB**. In AAOP , OA = OP ( radii ) .. LOPA = LOAP . Now QOA is an exterior of △ AOP , .. L QOA = LOPA + LOAP = 24 OPA . I. 12 . I. 8 , Cor . 1 . CASE II . Sim1 QOB .. 4 QOA + 4 QOB = 24 OPB , 2 ( 4 OPA + 4 OPB ) , .. LAOB = 2**LAPB**...### Other editions - View all

Elementary Geometry: Practical and Theoretical Charles Godfrey,Arthur Warry Siddons No preview available - 2015 |

### Common terms and phrases

AABC altitude base BC bisects Calculate centimetres centre chord circle of radius circumcentre circumcircle circumference circumscribed common tangent concyclic Constr Construct a triangle Construction Proof cyclic quadrilateral Data diagonal diameter distance divided Draw a circle Draw a straight equal circles equiangular equidistant equilateral triangle equivalent find a point Find the area fixed point Give a proof given circle given line given point given straight line hypotenuse inch paper inscribed intersect isosceles trapezium isosceles triangle LAOB LAPB locus of points Measure mid-point miles opposite sides parallelogram Plot the locus polygon produced protractor Q. E. D. Ex quadrilateral ABCD radii rect rectangle rectangle contained reflex angle Repeat Ex rhombus right angles right-angled triangle segment set square similar triangles subtends tangent THEOREM trapezium triangle ABC units of length vertex vertical angle

### Popular passages

Page 88 - If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent.

Page 269 - To describe an isosceles triangle, having each of the angles at the base double of the third angle.

Page 206 - If a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.

Page 342 - Pythagoras' theorem states that the square of the length of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the lengths of the other two sides.

Page 270 - If a straight line touch a circle, and from the point of contact a chord be drawn, the angles which this chord makes with the tangent are equal to the angles in the alternate segments.

Page 186 - This sub-division shows that the square on the hypotenuse of the above right-angled triangle is equal to the sum of the squares on the sides containing the right angle.

Page 206 - 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 on the line between the points of section, is equal to the square on half the line.

Page 136 - 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.

Page 214 - A point moves so that the sum of the squares of its distances from the points (0, 0), (1, 0) is constant.

Page 123 - The difference between any two sides of a triangle is less than the third side.