The Elements of Euclid for the Use of Schools and CollegesMacmillan, 1872 - 400 Seiten |
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Seite 5
... . That a terminated straight line may be produced to any length in a straight line : 3. And that a circle may be described from any centre , at any distance from that centre . } AXIOMS . 1. Things which are equal to the DEFINITIONS . 5.
... . That a terminated straight line may be produced to any length in a straight line : 3. And that a circle may be described from any centre , at any distance from that centre . } AXIOMS . 1. Things which are equal to the DEFINITIONS . 5.
Seite 7
... , AB , BC are equal to one another . Wherefore the triangle ABC is equilateral , and it is described on the given straight line AB . [ Axiom 1 . [ Def . 24 . Q.E.F. PROPOSITION 2. PROBLEM . From a given point to draw.
... , AB , BC are equal to one another . Wherefore the triangle ABC is equilateral , and it is described on the given straight line AB . [ Axiom 1 . [ Def . 24 . Q.E.F. PROPOSITION 2. PROBLEM . From a given point to draw.
Seite 44
... a parallelogram FECG has been described equal to the given triangle ABC , and having one of its angles CEF equal to the given angle D. Q.E.F. PROPOSITION 43. THEOREM . The complements of the parallelograms which 44 EUCLID'S ELEMENTS .
... a parallelogram FECG has been described equal to the given triangle ABC , and having one of its angles CEF equal to the given angle D. Q.E.F. PROPOSITION 43. THEOREM . The complements of the parallelograms which 44 EUCLID'S ELEMENTS .
Seite 49
... described on the given straight line AB . Q.E.F. COROLLARY . From the demonstration it is manifest that every parallelogram which has one right angle has all its angles right angles . PROPOSITION 47. THEOREM . In any right - angled ...
... described on the given straight line AB . Q.E.F. COROLLARY . From the demonstration it is manifest that every parallelogram which has one right angle has all its angles right angles . PROPOSITION 47. THEOREM . In any right - angled ...
Seite 50
... described on the sides which contain the right angle . Let ABC be a right - angled triangle , having the right angle BAC : the square described on the side BC shall be equal to the squares described on the sides BA , AC . On BC describe ...
... described on the sides which contain the right angle . Let ABC be a right - angled triangle , having the right angle BAC : the square described on the side BC shall be equal to the squares described on the sides BA , AC . On BC describe ...
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ABCD AC is equal angle ABC angle ACB angle BAC angle EDF angles equal Axiom base BC 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