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 TrigonometryW. E. Dean, 1851 - 317 σελίδες |
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Σελίδα 11
... greater than its part . 10. All right angles are equal to one another . 11. " Two straight lines which intersect one another , cannot be both pa- " rallel to the same straight line . " PROPOSITION I. PROBLEM . To describe an equilateral ...
... greater than its part . 10. All right angles are equal to one another . 11. " Two straight lines which intersect one another , cannot be both pa- " rallel to the same straight line . " PROPOSITION I. PROBLEM . To describe an equilateral ...
Σελίδα 13
... greater . It is required to cut off from AB , the greater , a part equal to C , the less . From the point A draw ( 2. 1. ) the straight line AD equal to C ; and from the centre A , and at the distance AD , describe ( 3. Post . ) the ...
... greater . It is required to cut off from AB , the greater , a part equal to C , the less . From the point A draw ( 2. 1. ) the straight line AD equal to C ; and from the centre A , and at the distance AD , describe ( 3. Post . ) the ...
Σελίδα 15
... greater than the other : Let AB be the greater , and from it cut ( 3. 1. ) off DB equal to AC the less , and join DC ; therefore , because in the tri- angles DBC , ACB , DB is equal to AC , and BC common to both , the two sides DB , BC ...
... greater than the other : Let AB be the greater , and from it cut ( 3. 1. ) off DB equal to AC the less , and join DC ; therefore , because in the tri- angles DBC , ACB , DB is equal to AC , and BC common to both , the two sides DB , BC ...
Σελίδα 16
... greater than it ; which is impossi- ble . 4 E But if one of the vertices , as D , be within the other triangle ACB ... greater than the angle BCD ; wherefore the angle FDC is likewise greater than BCD ; much more then is the angle BDC ...
... greater than it ; which is impossi- ble . 4 E But if one of the vertices , as D , be within the other triangle ACB ... greater than the angle BCD ; wherefore the angle FDC is likewise greater than BCD ; much more then is the angle BDC ...
Σελίδα 20
... greater , which is im- possible ; therefore BE is not in the same straight line with BC . And in like manner , it ... greater than either of the interior , and opposite angles . Let ABC be a triangle , and let its side BC be produced to ...
... greater , which is im- possible ; therefore BE is not in the same straight line with BC . And in like manner , it ... greater than either of the interior , and opposite angles . Let ABC be a triangle , and let its side BC be produced to ...
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ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC base BC bisected centre chord circle ABC circumference cosine cylinder demonstrated described diameter divided draw equal and similar equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given rectilineal 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 PROB PROP proportional 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 touches the circle triangle ABC triangle DEF wherefore