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 36
... Corollary 2 . Therefore all the interior angles of the figure , together with four right angles , are equal to twice as many right angles as the figure has sides . COROLLARY 2. All the exterior angles of any recti- lineal figure are ...
... Corollary 2 . Therefore all the interior angles of the figure , together with four right angles , are equal to twice as many right angles as the figure has sides . COROLLARY 2. All the exterior angles of any recti- lineal figure are ...
Seite 48
... COROLLARY . From this it is manifest , how to a given straight line , to apply a parallelogram , which shall have an angle equal to a given rectilineal angle , and shall be equal to a given rectilineal figure ; namely , by applying to ...
... COROLLARY . From this it is manifest , how to a given straight line , to apply a parallelogram , which shall have an angle equal to a given rectilineal angle , and shall be equal to a given rectilineal figure ; namely , by applying to ...
Seite 49
... 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 triangle BOOK I. 46 . 49.
... 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 triangle BOOK I. 46 . 49.
Seite 56
... COROLLARY . From the demonstration it is manifest , that parallelograms about the diameter of a square are likewise squares . PROPOSITION 5 . THEOREM . If a straight line be divided into two equal parts and also into two unequal parts ...
... COROLLARY . From the demonstration it is manifest , that parallelograms about the diameter of a square are likewise squares . PROPOSITION 5 . THEOREM . If a straight line be divided into two equal parts and also into two unequal parts ...
Seite 57
... Corollary . and DF together with CH is the gnomon CMG ; therefore the gnomon CMG is equal to the rectangle AD , DB . To each of these add LG , which is equal to the square on CD . [ II . 4 , Corollary , and I. 34 . Therefore the gnomon ...
... Corollary . and DF together with CH is the gnomon CMG ; therefore the gnomon CMG is equal to the rectangle AD , DB . To each of these add LG , which is equal to the square on CD . [ II . 4 , Corollary , and I. 34 . Therefore the gnomon ...
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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