## Elements of Geometry |

### From inside the book

Results 1-5 of 47

Page vii

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**example**of Euclid , and this order cannot fail of being good , if the propositions are well connected together . This section also is followed by a series of problems relating to the objects of which it treats . The fourth section ... Page x

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**example**, as it is between 16 , the square of 4 , and 25 , the square of 5 , has for its root a number comprehended between 4 and 5 , but which cannot be exactly assigned . In like manner 89 , which is between 64 , the cube of 4 , and ... Page xi

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**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 with the antecedent , this last will be contained ... Page xii

... of the two last is to their difference . For

... of the two last is to their difference . For

**example**, 6 + 4 : 6 --- 4 : 18+ 12 : 18 10 : 2 : 30 : 6 . - 12 , or When the proportion A : B :: C : D is changed into A : C :: B : D , A and B are the antecedents , C and D xii Introduction . Page xiv

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**example**, in the proportion A : B :: C : D , A , B , C , D , denote certain lines , we can always suppose one of these lines , or a fifth , if we please , to answer as a common measure to the whole , and to be taken for unity ; then A ...### 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