## New Plane and Solid Geometry |

### From inside the book

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**plane**as a surface such that if a straight line be drawn between any two of its points , it lies entirely in the surface . Thus , if P and Q are any two points in sur- face**MN**, and the straight line PQ lies entirely in the surface , then ... Page 33

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**MN**is drawn ; if through points C and D on AB equidistant from 0 , parallels to**MN**be drawn , the tri- angles formed are equal . M A- -B D N 2 管 PROP . XVIII . THEOREM 78. ( Converse RECTILINEAR FIGURES 33. Page 131

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**m n**AH HB 5. In △ ABF , = AE 20 ( 1 ) ( ? ) ; whence , equation ( 1 ) . ( ? ) Ex . 68. Construct a fourth proportional to three lines whose lengths are 8 , 9 , and 12 , respectively . Ex . 69. Construct a fourth proportional to 12 , 8 ... Page 136

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**M N**To Prove ( 1 ) N a'x b ' b b ' R Proof . 1. Let R be a rect . with altitude a and base b ' . = 2. M and R have altitudes ; and bases b and b ' , respec- tively ; find ratio M to R by § 275 . 3. R and N have bases ; and altitudes a ... Page 137

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**M N**( 1 ) ( § 277 ) 2. N being unit of surface , is area of M ; whence equa- tion ( 1 ) . Note . The statement of Prop . III is an abbreviation of the following : If the unit of surface is a square whose side is the linear unit , the ...### Other editions - View all

### Common terms and phrases

ABC and A'B'C adjacent angles altitude angle formed angles are equal apothem arc BC base and altitude bisector bisects centre chord circle circumference circumscribed coincide construct Converse of Prop diagonals diameter diedral angle distance Draw line equal parts occur equal respectively equally distant equilateral triangle exterior angle faces frustum Given line given point homologous sides hypotenuse intersecting isosceles trapezoid isosceles triangle LAOB lateral area lateral edges line drawn lines be drawn measured by arc middle point number of sides oblique lines opposite parallel parallelogram parallelopiped perimeter perpendicular plane MN polyedron prism Proof proportional Prove pyramid quadrilateral radii radius rectangle regular polygon rhombus right angles right triangle secant segments slant height spherical polygon spherical triangle square straight line surface tangent tetraedron THEOREM trapezoid triedral vertex vertices volume