## Elements of Geometry |

### From inside the book

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**plane**and another part without it . Demonstration . By the definition of a ...**planes**cut each other , their common intersection is a straight line ...**MN**, it will be perpendicular to every other straight line PQ drawn 106 ... Page 107

... plane , and thus it will be perpendicular to the

... plane , and thus it will be perpendicular to the

**plane MN**. Demonstration . Through a point Q , taken at pleasure in PQ , draw the straight line BC in the angle BPC making BQ = QC ( 242 ) ; join AB , AQ , AC . The base BC being bisected ... Page 108

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**plane MN**. It is manifest that this incli- nation is the same for all the oblique lines AB , AC , AD , & c . , which depart equally from the perpendicular ; for all the trian- gles ABP , ACP , ADP , & c . , are equal . THEOREM . 332 ... Page 109

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**plane**. The least distance of these lines is the straight line PD , which is at the same time perpendicular to the ...**MN**, Fig . 186 . every line DE parallel to AP will be perpendicular to the same**plane**. Demonstration . Let there be a ... Page 110

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**plane MN**, it will be parallel to this plane . Demonstration . If the line AB , which is in the plane ABCD , should meet the**plane MN**, this can take place only in some point of the line CD , the common intersection of the two planes ...### 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