The Elements of Euclid, books i-vi; xi. 1-21; xii. 1,2; ed. by H.J. Hose, Book 1 |
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Page 155
... former magnitudes are called " equimultiples " of the latter . III . Ratio is a mutual relation of two magnitudes of the same kind to one another in respect of quantity . OBS . It appears that for one magnitude to have BOOK V.
... former magnitudes are called " equimultiples " of the latter . III . Ratio is a mutual relation of two magnitudes of the same kind to one another in respect of quantity . OBS . It appears that for one magnitude to have BOOK V.
Page 156
... equimultiples whatever , and of the second and fourth any equimultiples whatever , the multiple of the third is greater than , equal to , or less than the multiple of the fourth , according as the multiple of the first is greater than , ...
... equimultiples whatever , and of the second and fourth any equimultiples whatever , the multiple of the third is greater than , equal to , or less than the multiple of the fourth , according as the multiple of the first is greater than , ...
Page 157
... equimultiples of the first and third , and such equimultiples of the second and fourth , that the multiple of the first shall be greater than the multiple of the second , but the multiple of the third not greater than the multiple of ...
... equimultiples of the first and third , and such equimultiples of the second and fourth , that the multiple of the first shall be greater than the multiple of the second , but the multiple of the third not greater than the multiple of ...
Page 160
... equal to the magnitude of which it is the multiple . AXIOMS . I. Equimultiples of the same magnitude , or of equal magnitudes , are equal to one another . II . Magnitudes , of which the same magnitude is an equimultiple , or of which equal ...
... equal to the magnitude of which it is the multiple . AXIOMS . I. Equimultiples of the same magnitude , or of equal magnitudes , are equal to one another . II . Magnitudes , of which the same magnitude is an equimultiple , or of which equal ...
Page 161
... equi- multiples of the two E , F. Then whatever multiple AB is of E , the same multiple shall AB and CD together be of E and F together . Since by hyp AB , CD are equimultiples of E , F , there are as many magnitudes in AB , each equal ...
... equi- multiples of the two E , F. Then whatever multiple AB is of E , the same multiple shall AB and CD together be of E and F together . Since by hyp AB , CD are equimultiples of E , F , there are as many magnitudes in AB , each equal ...
Common terms and phrases
ABC is equal adjacent angles angle ABC angle ACB angle BAC angle DEF angle EDF angles are equal angular points base BC bisected centre circle ABC circle DEF circumference const cut the circle diagonal draw equal angles equal Ax equals add equi equimultiples exterior angle FGHKL fore four magnitudes fourth given straight line gnomon hence the angle homologous hyps included angle interior and opposite join less Let ABC multiple opposite angle parallelogram perpendicular produced PROP proportional proved radius rectangle contained remaining angle respectively equal right angles segment shewn sides BC similar solid angle square of AC THEOR thing are equal third angle three angles touching the circle triangle ABC unequal
Popular passages
Page 39 - To draw a straight line through a given point parallel to a given straight line. Let A be the given point, and BC the given straight line...
Page 52 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Page 16 - To draw a straight line at right angles to a given straight line, from a given point in the same.
Page 5 - From a given point to draw a straight line equal to a given straight line. Let A be the given point, and BC the given straight line ; it is required to draw, from the point A, a straight line equal to BC.
Page 11 - Upon the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated in one extremity of' the base, equal to one another, and likewise those which are terminated in the other extremity.
Page 105 - If a straight line touch a circle, and from the point of contact a straight line be drawn cutting the circle ; the angles which this line makes with the line touching the circle, shall be equal to the angles which are in the alternate segments of the circle.
Page 118 - IF a straight line touch a circle, and from the point of contact a straight line be drawn at right angles to the touching line, the centre of the circle shall be in that line.
Page 66 - If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line.
Page 6 - From the greater of two given straight lines to cut off a part equal to the less. Let AB and C be the two given straight lines, whereof AB is the greater.
Page 119 - Upon a given straight line to describe a segment of a circle, which shall contain an angle equal to a given rectilineal angle.