The Elements of Euclid for the Use of Schools and Colleges: Comprising the First Six Books and Portions of the Eleventh and Twelfth BooksMacmillan, 1886 - 400 Seiten |
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Seite 1
... lies wholly in that superficies . 8. A plane angle is the inclination of two lines to one another in a plane , which meet together , but are not in the same direction . 9. A plane rectilineal angle is the inclination of two 1.
... lies wholly in that superficies . 8. A plane angle is the inclination of two lines to one another in a plane , which meet together , but are not in the same direction . 9. A plane rectilineal angle is the inclination of two 1.
Seite 2
... meet together , but are not in the same straight line . Note . When several angles are at one point B , any one of them is expressed by three letters , of which the letter which is at the vertex of the angle , that is , at the point at ...
... meet together , but are not in the same straight line . Note . When several angles are at one point B , any one of them is expressed by three letters , of which the letter which is at the vertex of the angle , that is , at the point at ...
Seite 6
... meet two straight lines , so as to make the two interior angles on the same side of it taken together less than two right angles , these straight lines , being continually produced , shall at length meet on that side on which are the ...
... meet two straight lines , so as to make the two interior angles on the same side of it taken together less than two right angles , these straight lines , being continually produced , shall at length meet on that side on which are the ...
Seite 24
... meet AC at E. Because two sides of a triangle are greater than the third side , the two sides BA , AE of the triangle ABE are greater than the side BE . To each of these add EC . Therefore BA , AC are greater than BE , EC . [ I. 20 ...
... meet AC at E. Because two sides of a triangle are greater than the third side , the two sides BA , AE of the triangle ABE are greater than the side BE . To each of these add EC . Therefore BA , AC are greater than BE , EC . [ I. 20 ...
Seite 31
... meet either towards B , D or towards A , C. Let them be pro- duced and meet towards B , D at the point G. A E G Therefore GEF is a triangle , and its exterior angle AEF is greater than the interior opposite angle EFG ; [ I. 16 . But the ...
... meet either towards B , D or towards A , C. Let them be pro- duced and meet towards B , D at the point G. A E G Therefore GEF is a triangle , and its exterior angle AEF is greater than the interior opposite angle EFG ; [ I. 16 . But the ...
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Häufige Begriffe und Wortgruppen
ABCD angle ABC angle ACB angle BAC angle EDF angles equal Axiom base BC BC is equal bisects the angle centre chord circle ABC circle described circumference Construction Corollary describe a circle diameter double draw a straight equal angles equal to F equiangular equilateral equimultiples Euclid Euclid's Elements exterior angle given circle given point given straight line gnomon Hypothesis inscribed intersect isosceles triangle less Let ABC magnitudes middle point multiple opposite angles opposite sides parallelogram perpendicular plane polygon produced proportionals PROPOSITION 13 Q.E.D. PROPOSITION quadrilateral radius rectangle contained rectilineal figure remaining angle rhombus right angles right-angled triangle segment shew shewn side BC square on AC straight line &c straight line drawn tangent THEOREM touches the circle triangle ABC triangle DEF twice the rectangle vertex Wherefore