## Elements of Geometry and Trigonometry |

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REVISED AND ABRIDGED BY CHARLES DAVIES , PROFESSOR OF MATHEMATICS IN THE MILITARY ACADEMY , AND AUTHOR OF THE

REVISED AND ABRIDGED BY CHARLES DAVIES , PROFESSOR OF MATHEMATICS IN THE MILITARY ACADEMY , AND AUTHOR OF THE

**COMMON**SCHOOL ARITHMETIC , DESCRIPTIVE GEOMETRY , ELEMENTS OF SURVEYING , AND A TREATISE ON SHADOWS AND PERSPECTIVE . Page 12

The

The

**common**name , proposition , is applied indifferently , to theorems , problems , and lemmas . A corollary is an obvious consequence , deduced from one or several propositions . A scholium is a remark on one or several preceding ... Page 14

THEOREM .. straight lines , which have two points

THEOREM .. straight lines , which have two points

**common**, coincide with each other throughout their whole extent , and form one and the same straight line . Let A and B be the two**common**points . In the first place it is evident that ... Page 15

If a straight line meet two other straight lines at a

If a straight line meet two other straight lines at a

**common**point , making the sum of the two adjacent angles equal to twó right angles , the two straight lines which are met , will form one and the same straight line . Page 20

Then , the triangles BAD , DAC , will have all the sides of the one equal to those of the other , each to each ; for BA is equal to AC , by hypothesis ; AD is

Then , the triangles BAD , DAC , will have all the sides of the one equal to those of the other , each to each ; for BA is equal to AC , by hypothesis ; AD is

**common**, and BD is equal to DC by construction : therefore , by the last ...### What people are saying - Write a review

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### Common terms and phrases

ABCD adjacent altitude base become Book called centre chord circle circumference circumscribed common cone consequently construction contained corresponding cosine Cotang cylinder described diameter difference distance divided draw drawn equal equation equivalent evident expressed extremities fall figure follows formed formulas four frustum give given gles greater half hence homologous included inscribed intersection less likewise logarithm manner means measured meet middle multiplied opposite parallel parallelogram parallelopipedon pass perpendicular plane polygon prism PROBLEM Prop proportional PROPOSITION pyramid quantities radii radius ratio reason rectangle regular remaining right angles Scholium segment shown sides similar sine solid solid angle sphere spherical triangle square straight line Suppose surface taken tang tangent THEOREM third triangle triangle ABC vertex whole