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 xv
... less than two right angles . After the general enunciation follows the discussion of the proposition . First , the enunciation is repeated and applied to the particular figure which is to be considered ; as for example , Let AB be the ...
... less than two right angles . After the general enunciation follows the discussion of the proposition . First , the enunciation is repeated and applied to the particular figure which is to be considered ; as for example , Let AB be the ...
Seite 2
... called a perpendicular to it . 11. An obtuse angle is that which is greater than a right angle . 12. An acute angle is that which is less than a right angle . A term or boundary is the extremity of any thing 2 EUCLID'S ELEMENTS .
... called a perpendicular to it . 11. An obtuse angle is that which is greater than a right angle . 12. An acute angle is that which is less than a right angle . A term or boundary is the extremity of any thing 2 EUCLID'S ELEMENTS .
Seite 6
... less than two right angles , these straight lines , being continually produced , shall at length meet on that side on which are the angles which are less than two right angles . PROPOSITION 1. PROBLEM . To describe an equilateral ...
... less than two right angles , these straight lines , being continually produced , shall at length meet on that side on which are the angles which are less than two right angles . PROPOSITION 1. PROBLEM . To describe an equilateral ...
Seite 8
... Q.E.F. PROPOSITION 3. PROBLEM . From the greater of two given straight lines to cut off a part equal to the less Let AB and C be the two given straight lines , of which AB is the greater : it is required to cut 8 EUCLID'S ELEMENTS .
... Q.E.F. PROPOSITION 3. PROBLEM . From the greater of two given straight lines to cut off a part equal to the less Let AB and C be the two given straight lines , of which AB is the greater : it is required to cut 8 EUCLID'S ELEMENTS .
Seite 9
... less . From the point A draw the straight line AD equal to C ; [ I. 2 . and from the centre A , at the distance AD , describe the circle DEF meeting AB at E. [ Postulate 3 . AE shall be equal to C. F Because the point A is the centre of ...
... less . From the point A draw the straight line AD equal to C ; [ I. 2 . and from the centre A , at the distance AD , describe the circle DEF meeting AB at E. [ Postulate 3 . AE shall be equal to C. F Because the point A is the centre of ...
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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