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 x
... problems which may naturally suggest themselves , but of which the solutions are not very obvious . The work finishes with a collection of exercises . Geo- metrical deductions afford a most valuable discipline for a student of ...
... problems which may naturally suggest themselves , but of which the solutions are not very obvious . The work finishes with a collection of exercises . Geo- metrical deductions afford a most valuable discipline for a student of ...
Seite xv
... problem , or to furnish assistance in the demonstration of the theorem . Lastly , we have the demonstration itself , which shews that the problem has been solved , or that the theorem is true . Sometimes , however , no construction is ...
... problem , or to furnish assistance in the demonstration of the theorem . Lastly , we have the demonstration itself , which shews that the problem has been solved , or that the theorem is true . Sometimes , however , no construction is ...
Seite xvi
... problem , and the letters Q.E.D. at the end of the discussion of a theorem . Q.E.F. is an abbreviation for quod erat faciendum , that is , which was to be done ; and Q.E.D. is an abbreviation for quod erat demonstrandum , that is ...
... problem , and the letters Q.E.D. at the end of the discussion of a theorem . Q.E.F. is an abbreviation for quod erat faciendum , that is , which was to be done ; and Q.E.D. is an abbreviation for quod erat demonstrandum , that is ...
Seite 6
... 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 triangle on 6 CO EUCLID'S ELEMENTS .
... 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 triangle on 6 CO EUCLID'S ELEMENTS .
Seite 7
... 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 , describe the ...
... 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 , describe 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