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 2
... draw one line perpendicular to another ; or to divide a line into two equal parts . A 9. Solution of a problem is ... drawn immediately from some proposition or other premises . 12. A Scholium is a remark or observation made on some ...
... draw one line perpendicular to another ; or to divide a line into two equal parts . A 9. Solution of a problem is ... drawn immediately from some proposition or other premises . 12. A Scholium is a remark or observation made on some ...
Página 18
... drawn from a point , situated with- out a straight line , to that line : any two oblique lines drawn from the samę point on different sides of the perpendicular , cutting off equal distances on the other line , will be equal ; and any ...
... drawn from a point , situated with- out a straight line , to that line : any two oblique lines drawn from the samę point on different sides of the perpendicular , cutting off equal distances on the other line , will be equal ; and any ...
Página 23
... draw CE parallel to the straight line AB ; and because AB is parallel to CE , and AC meets them , the al- ternate ... drawing straight lines from a point F within the figure to each of its angles . And , by the preceding proposition ...
... draw CE parallel to the straight line AB ; and because AB is parallel to CE , and AC meets them , the al- ternate ... drawing straight lines from a point F within the figure to each of its angles . And , by the preceding proposition ...
Página 28
... draw BE parallel to CA ; and through C draw CF parallel to BD : There- fore , each of the figures EBCA , DBCF is a parallelogram ; and EBCA is equal ( 29. 1. ) to DBCF , because they are upon the same base BC , and between the same pa ...
... draw BE parallel to CA ; and through C draw CF parallel to BD : There- fore , each of the figures EBCA , DBCF is a parallelogram ; and EBCA is equal ( 29. 1. ) to DBCF , because they are upon the same base BC , and between the same pa ...
Página 32
... 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 point A , a straight line equal to BC . From the point A to B draw ( 1. Post . ) the ...
... 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 point A , a straight line equal to BC . From the point A to B draw ( 1. Post . ) the ...
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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