## Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle and the Geometry of Solids ; to which are Added Elements of Plane and Spherical Trigonometry |

### From inside the book

Page 18

...

...

**Spherical**Trigonometry John Playfair. A B D E C N. B. When several**angles**are at one point B , any one of them ' is expressed by three letters , of which the letter that is at the ver- ' tex of the**angle**, that is , at the point in which ... Page 24

...

...

**Spherical**Trigonometry John Playfair. posite , shall be equal , each to each , viz . the**angle**ABC to the**angle**DEF , and the**angle**ACB to DFE . For , if the triangle ABC be applied to the triangle DEF , so that the point A may be on D ... Page 25

...

...

**Spherical**Trigonometry John Playfair ! A remainder CG ; and FC was proved to be equal to GB , therefore the two sides BF , FC are equal to the two CG , GB , each to each ; but the**angle**BFC is equal to the**angle**CGB ; wherefore the ... Page 26

...

...

**Spherical**Trigonometry John Playfair. B , cannot be equal to one another . Join CD , and if possible let CB be equal ...**angle**ACD is equal ( 5. 1. ) to the**angle**ADC : But the**angle**ACD is greater than the**angle**BCD ; there- C D ... Page 27

...

...

**Spherical**Trigonometry John Playfair. B A DG C E F to DF ; and also the base BC equal to the base EF . The**angle**BAC is equal to the**angle**EDF . For , if the triangle ABC be applied to the triangle DEF , so that the point B be on E , and ...### Other editions - View all

### Common terms and phrases

ABC is equal ABCD altitude angle ABC angle ACB angle BAC angle EDF arch AC base BC bisected centre circle ABC circumference cosine cylinder definition demonstrated diameter draw equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater hypotenuse inscribed join less Let ABC Let the straight line BC magnitudes MDCCCXX meet multiple opposite angle parallel parallelepipeds parallelogram perpendicular polygon prism PROB produced proportionals proposition Q. E. D. COR Q. E. D. PROP radius ratio rectangle contained rectilineal figure remaining angle segment semicircle shewn side BC sine solid angle solid parallelepipeds spherical angle spherical triangle straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore