Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle, and the Geometry of Solids; to which are Added, Elements of Plane and Spherical TrigonometryB. & S. Collins; W. E. Dean, printer, 1836 - 311 páginas |
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Página 7
... line may be produced to any length in a straight line . 3. And that a circle may be described from any centre , at any distance from that centre . AXIOMS . 1. THINGS which are equal to the same OF GEOMETRY . BOOK I. 7.
... line may be produced to any length in a straight line . 3. And that a circle may be described from any centre , at any distance from that centre . AXIOMS . 1. THINGS which are equal to the same OF GEOMETRY . BOOK I. 7.
Página 30
... described upon the side sub- tending the right angle , is equivalent to the squares described upon the sides which contain the right angle . Let ABC be a right angled trian- gle having the right angle BAC ; the square described upon the ...
... described upon the side sub- tending the right angle , is equivalent to the squares described upon the sides which contain the right angle . Let ABC be a right angled trian- gle having the right angle BAC ; the square described upon the ...
Página 31
... described upon one of the sides of a triangle , be equivalent to the squares described upon the other two sides of it ; the angle contained by these two sides is a right angle . If the square described upon BC , one of the sides of the ...
... described upon one of the sides of a triangle , be equivalent to the squares described upon the other two sides of it ; the angle contained by these two sides is a right angle . If the square described upon BC , one of the sides of the ...
Página 32
... described upon the given straight line AB . PROP . II . PROB . From a given point to draw a straight line equal to a given straight line . Let A be the given point , and BC the gi- ven straight line ; it is required to draw , from the ...
... described upon the given straight line AB . PROP . II . PROB . From a given point to draw a straight line equal to a given straight line . Let A be the given point , and BC the gi- ven straight line ; it is required to draw , from the ...
Página 37
... described from A as a centre , with a radius equal to AB , the other given side , would cut BC on opposite sides of C ' ; so that only one obtuse angled triangle could be B A formed ; that is , the triangle BC'A will be thè triangle ...
... described from A as a centre , with a radius equal to AB , the other given side , would cut BC on opposite sides of C ' ; so that only one obtuse angled triangle could be B A formed ; that is , the triangle BC'A will be thè triangle ...
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ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC angles equal base BC bisected centre chord circle ABC circumference cosine cylinder demonstrated diameter divided equal and similar equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater Hence hypotenuse inscribed join less Let ABC Let the straight magnitudes meet multiple opposite angle parallel parallelogram parallelopiped perpendicular polygon prism PROP proposition quadrilateral radius ratio rectangle contained rectilineal figure remaining angle right angled triangle SCHOLIUM segment semicircle shewn side BC sine solid angle solid parallelopiped spherical angle spherical triangle square straight line BC THEOR third touches the circle triangle ABC triangle DEF wherefore