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
... propositions . The propositions are of two kinds , pro- blems and theorems . In a problem something is required to be done ; in a theorem some new principle is asserted to be true . A proposition consists of various parts . We have ...
... propositions . The propositions are of two kinds , pro- blems and theorems . In a problem something is required to be done ; in a theorem some new principle is asserted to be true . A proposition consists of various parts . We have ...
Seite xvi
... proposition itself . The word hypothesis is used in the same sense as supposition . To assist the student in following the steps of the reasoning , references are given to the results already ob- tained which are required in the ...
... proposition itself . The word hypothesis is used in the same sense as supposition . To assist the student in following the steps of the reasoning , references are given to the results already ob- tained which are required in the ...
Seite 7
... PROPOSITION 1. PROBLEM . To describe an equilateral triangle on a given finite straight line . Let AB be the given straight line : it is required to describe an equilateral triangle on AB . A A From the centre A , at the distance AB ...
... PROPOSITION 1. PROBLEM . To describe an equilateral triangle on a given finite straight line . Let AB be the given straight line : it is required to describe an equilateral triangle on AB . A A From the centre A , at the distance AB ...
Seite 8
... PROPOSITION 2. PROBLEM . From a given point to draw a straight line equal to a given straight line . Let A be the given point , and BC the given straight line : it is required to draw from the point A a straight line equal to BC . From ...
... PROPOSITION 2. PROBLEM . From a given point to draw a straight line equal to a given straight line . Let A be the given point , and BC the given straight line : it is required to draw from the point A a straight line equal to BC . From ...
Seite 12
... PROPOSITION 6. THEOREM . If two angles of a triangle be equal to one another , the sides also which subtend , or are oppo- site to , the equal angles , shall be equal to one another . Let ABC be a triangle , having the angle ABC equal ...
... PROPOSITION 6. THEOREM . If two angles of a triangle be equal to one another , the sides also which subtend , or are oppo- site to , the equal angles , shall be equal to one another . Let ABC be a triangle , having the angle ABC equal ...
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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