## Elements of Geometry |

### From inside the book

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**solid**is that which unites the three dimensions of ex- ension . 9. When two straight lines AB , AC , ( fig . 2 ...**angle**; the point of meeting or intersection , A , is the vertex of the**angle**; the lines AB , AC , are its sides . An ... Page 69

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**angle**BE ; consequently the triangles are similar ; and they give the proportion , AB : CE :: AD : AC ; whence AB X ...**solid**, for a reason that will be given hereafter . The value of this product is easily conceived by supposing the ... Page 106

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**angle**DOE = ACI , and consequently the arc DE equal to the half side Al ; the polygon P : circle C :: triangle ACI ...**Solid**106 Elements of Geometry . Page 107

Adrien Marie Legendre. PART SECOND . SECTION FIRST . Of Planes and

Adrien Marie Legendre. PART SECOND . SECTION FIRST . Of Planes and

**Solid Angles**. DEFINITIONS . 313. A STRAIGHT line ... angle , or the mutual inclination of two planes , is the quantity , whether greater or less , by which they depart ... Page 109

... angle BPC , making BQ = QC ( 242 ) ; join AB , AQ , AC . The base BC being bisected at the point Q , the triangle BPC will give PC + PB = 2PQ + 2QC ( 194 ) . The triangle BAC will give , in like manner , AC + AB = 2AQ ...

... angle BPC , making BQ = QC ( 242 ) ; join AB , AQ , AC . The base BC being bisected at the point Q , the triangle BPC will give PC + PB = 2PQ + 2QC ( 194 ) . The triangle BAC will give , in like manner , AC + AB = 2AQ ...

**Solid Angles**. 109.### 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