## Elements of Geometry |

### From inside the book

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**plane**, and another part without it . Demonstration . By the definition of a piane ( 6 ) a straight line , which has ...**MN**, it will be perpendicular to every other straight 108 Elements of Geometry . Page 109

Adrien Marie Legendre. MN , it will be perpendicular to every other straight line PQ drawn through its foot in the same plane , and thus it will be per- pendicular to the

Adrien Marie Legendre. MN , it will be perpendicular to every other straight line PQ drawn through its foot in the same plane , and thus it will be per- pendicular to the

**plane MN**. Demonstration . Through a point Q , taken at pleasure ... Page 110

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**plane MN**. It is manifest that this in- clination 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 111

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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**, every line DE parallel to AP will be perpendicular to the same**plane**. Demonstration . Let there be a**plane**... Page 112

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**plane**; therefore , by the above corollary , they are parallel to each other . It is supposed that the three lines ...**MN**, it will be parallel to this**plane**. Demonstration . If the line AB , which is in the**plane**ABCD , should meet the ...### 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