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 6
... Magnitudes which coincide with one another , that is , which exactly fill the same space , are equal to one another . 9. The whole is greater than its part . 10. Two straight lines cannot enclose a space . 11. All right angles are equal ...
... Magnitudes which coincide with one another , that is , which exactly fill the same space , are equal to one another . 9. The whole is greater than its part . 10. Two straight lines cannot enclose a space . 11. All right angles are equal ...
Seite 134
... magnitudes of the same kind to one another in respect of quantity . 4. Magnitudes are said to have a ratio to one another , when the less can be multiplied so as to exceed the other . 5. The first of four magnitudes is said to have the ...
... magnitudes of the same kind to one another in respect of quantity . 4. Magnitudes are said to have a ratio to one another , when the less can be multiplied so as to exceed the other . 5. The first of four magnitudes is said to have the ...
Seite 135
... magnitudes are proportionals , the first is said to have to the third the duplicate ratio of that which it has to the second . Xis [ The second magnitude is said to be a mean propor- tional between the first and the third . ] 11. When ...
... magnitudes are proportionals , the first is said to have to the third the duplicate ratio of that which it has to the second . Xis [ The second magnitude is said to be a mean propor- tional between the first and the third . ] 11. When ...
Seite 136
... magnitude of proportionals , so that they continue still to be proportionals . 13. Permutando , or alternando , by ... magnitudes , as the first is to the last of the others . Of this there are the two following kinds , which 136 ...
... magnitude of proportionals , so that they continue still to be proportionals . 13. Permutando , or alternando , by ... magnitudes , as the first is to the last of the others . Of this there are the two following kinds , which 136 ...
Seite 137
... magnitudes are taken , two and two . 19. Ex æquali . This term is used simply by itself , when the first magnitude ... magnitudes , are equal to one another . 2. Those magnitudes , of which the same or equal mag- nitudes are ...
... magnitudes are taken , two and two . 19. Ex æquali . This term is used simply by itself , when the first magnitude ... magnitudes , are equal to one another . 2. Those magnitudes , of which the same or equal mag- nitudes are ...
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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