## Elements of Geometry and Trigonometry |

### From inside the book

Results 1-5 of 13

Page 128

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**plane**AB , and also wholly in the**plane**CD ( Book I. Def . 6. ) : therefore it will be in both**planes**at once , and ...**MN**be the**plane**of the two lines BB , CC , and let AP be perpendicular to them at their point of intersection P ... Page 129

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**plane MN**. Cor . 2. At a given point P on a plane , it is impossible to erect more than one perpendicular to that plane ; for if there could be two perpendiculars at the same point P , draw through these two perpendiculars a plane ... Page 130

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**plane MN**; which inclination is evidently equal with respect to all such lines AB , AC , AD , as are equally distant from the perpendicular ; for all the triangles ABP , ACP , ADP , & c . are equal to each other . PROPOSITION VI ... Page 131

... plane APD , since BC is at once perpendicular to the two straight lines AD , PD . Scholium . The two lines AE , BC ... MN will be PD ; in the

... plane APD , since BC is at once perpendicular to the two straight lines AD , PD . Scholium . The two lines AE , BC ... MN will be PD ; in the

**plane MN**M P A E D B draw BC perpendicular to PD , and draw AŠ . By the Corollary of the ... Page 132

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**plane MN**, they will be par- allel ; for if they be not so , draw through the point D , a line parallel to AP , this par- allel will be perpendicular to the**plane MN**; therefore M P A E B through the same point D more than one ...### Other editions - View all

### Common terms and phrases

adjacent adjacent angles altitude angle ACB angle BAC ar.-comp base multiplied bisect Book centre chord circ circumference circumscribed common cone convex surface Cosine Cotang cylinder diagonal diameter dicular distance draw drawn equal angles equally distant equiangular equivalent figure formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed polygon intersection less Let ABC let fall logarithm measured by half number of sides oblique lines opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedron polygon ABCDE prism proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABC Scholium secant secant line segment side BC similar sine solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex