## 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 sider |

### Inni boken

Resultat 1-5 av 100

Side 4

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**less**considerable , it is hoped may in some degree facilitate the study of the Elements . Such are those made on the definitions in the first Book , and particularly on that of a straight line . A new axiom is also introduced in the ... Side 13

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**less**. Let AB and C be the two given straight lines , whereof AB is 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 ... Side 15

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**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 are equal to the two AC , CB , each to each ; but the angle DBC is also equal to the angle ACB ... Side 21

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**less**than two right angles . Let ABC be any triangle ; any two of its angles together are**less**than two right angles . A A Produce BC to D ; and because ACD is the exterior angle of the tri- angle ABC , ACD is greater ( 16. 1. ) than ... Side 22

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**less**than it ; it is not equal , because then the angle ABC would be equal ( 5. 1. ) to the angle ACB ; but it is not ; therefore AC is not equal to AB ; nei- ther is it**less**; because then the angle ABC would be**less**( 18. 1. ) than ...### Andre utgaver - Vis alle

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### Vanlige uttrykk og setninger

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