## Elements of Geometry |

### From inside the book

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**solid**is that which unites the three dimensions of ex- tension . 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 67

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**angle**BE ; consequently the triangles are similar ; and they give the proportion , AB : CE :: AD : AC ; whence ABX ...**solid**, for a reason that will be given hereafter . The value of this product . is easily conceived by supposing the ... Page 104

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**angle**DOE = ACI , and consequently the arc DE equal to the half side AI ; the polygon P : circle C :: triangle ACI ...**Solid**104 Elements of Geometry . - Page 105

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 from ... Page 107

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

**Solid Angles**. 107.### Other editions - View all

### Common terms and phrases

ABC fig adjacent angles altitude angle ACB angle BAD 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 and parallel equiangular equilateral equivalent faces figure four right angles frustum Geom gles greater hence homologous sides hypothenuse inclination inscribed circle isosceles join less let fall line AC manner mean proportional measure the half meet multiplied number of sides oblique lines opposite parallelogram parallelopiped perimeter perpendicular plane MN polyedron prism proposition pyramid S-ABC quadrilateral radii radius ratio rectangle regular polygon right angles right-angled triangle Scholium segment semicircumference side BC similar solid angle sphere spherical polygons spherical triangle square described straight line tangent THEOREM three plane angles triangle ABC triangular prism triangular pyramids vertex vertices whence