The Elements: Books III-IXSt. John's College Press, 1949 - Mathematics, Greek |
From inside the book
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Page 126
... fourth : " Given four magnitudes in predetermined order , the first two homogeneous with one another , and likewise also the last two , the magnitudes are said to form a proportion ( or to be in proportion ) when any multiple of the ...
... fourth : " Given four magnitudes in predetermined order , the first two homogeneous with one another , and likewise also the last two , the magnitudes are said to form a proportion ( or to be in proportion ) when any multiple of the ...
Page 165
... four proportional magnitudes , so that , as A is to B , so is C to D. " In a number of expressions like this it is absolutely necessary , when translating Thus the Greek here is : into English , to interpolate words which are not in the ...
... four proportional magnitudes , so that , as A is to B , so is C to D. " In a number of expressions like this it is absolutely necessary , when translating Thus the Greek here is : into English , to interpolate words which are not in the ...
Page 183
... four magnitudes are of the same kind ; whereas v . 23 , the proposition now in question , is not subject to this restriction . Simson rightly observes that in the last step of the proof it should be stated that " G , K are any ...
... four magnitudes are of the same kind ; whereas v . 23 , the proposition now in question , is not subject to this restriction . Simson rightly observes that in the last step of the proof it should be stated that " G , K are any ...
Common terms and phrases
ABCD angle ABC angle BAC antecedent Aristotle base bisected centre circle ABC circumference construction continued proportion corresponding sides cube number definition diameter drawn enunciation equal angles equiangular equimultiples Euclid Eutocius ex aequali four magnitudes geometrical geometrical progression given circle given straight line greater ratio greatest common measure Heiberg hypothesis Iamblichus joined less mean proportional numbers measures the number multiple multitude Nicomachus odd number parallel parallelogram pentagon perpendicular polygon Porism prime number Proclus Prop proper fraction proposition PROPOSITION 13 proved rect rectangle rectangle contained rectilineal figure reductio ad absurdum remaining angle right angles segment semicircle similar and similarly similar plane numbers Simson solid numbers square number subtracted taken Theon Theon of Smyrna theorem touches the circle triangle ABC unit VIII δὲ καὶ πρὸς τὸ τοῦ