## Elements of Geometry |

### From inside the book

Results 1-5 of 100

Page xi

...

...

**consequently**a new proportion . Let there be , for example , the proportion we shall have or 46 12 18 , 644 18 12:12 , 10 : 4 :: 30 : 12 . 2. If from the consequent of a ratio we subtract the antece- dent , and compare the difference ... Page xii

...

...

**consequently**, B + A : D + C :: BA : D― C , or , by changing the place of the means , BA : B - A :: D + C : D - C ; that is , the sum of the two first terms of a proportion is to their difference as the sum of the two last is to their ... Page 4

...

...

**consequently**it falls upon CD , and the angle EGH upon ACD , and EGH is equal to ACD ; therefore all right angles are equal . THEOREM . 28. A straight line CD ( fig . 17 ) , which meets another straight line AB , makes with it two ... Page 14

...

...

**consequently**, the side C'B ' = AC , and the angle B'C'K = ACB , and the angle KB'C ' = CAI . = It hence follows , 1. that the angle AC'B ' , designated by C ' , is composed of two angles , equal , respectively , to the two angles B and ... Page 15

...

...

**consequently**, be less than any given angle ; it will hence be seen that the sum of the three angles of the triangle a'b'c ' reduces itself to the single angle c ' . In order to obtain the exact measure of this sum , let us pro- duce ...### Other editions - View all

### Common terms and phrases

ABC fig adjacent angles altitude angle ACB angle BAC base ABCD bisect centre chord circ circular sector circumference circumscribed common cone consequently construction convex surface Corollary cube cylinder Demonstration diagonals diameter draw drawn equal angles equiangular equilateral equivalent faces figure formed four right angles frustum GEOM given point gles greater hence homologous sides hypothenuse inclination intersection isosceles triangle JOHN CRERAR LIBRARY join less Let ABC let fall line AC mean proportional measure the half meet multiplied number of sides oblique lines opposite parallelogram parallelopiped perimeter perpendicular plane MN polyedron prism produced proposition radii radius ratio rectangle regular polygon right angles Scholium sector segment semicircle semicircumference side BC similar solid angle sphere spherical polygons spherical triangle square described straight line tangent THEOREM three angles triangle ABC triangular prism triangular pyramids vertex vertices whence