The Elements of Euclid,: In which the Propositions are Demonstrated in a New and Shorter Manner Than in Former Translations, and the Arrangement of Many of Them Altered, to which are Annexed Plain and Spherical Trigonometry, Tables of Logarithms from 1 to 10000, and Tables of Sines, Tangents, and Secants, Both Natural and ArtificialJ. Murray, no. 32. Fleetstreet; and C. Elliot, Parliament-square, Edinburgh., 1776 - 264 sider |
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Side ix
... 11. book V. by Mr Simpson . The 5th and 6th propofitions are joined in one , as also the 14th and 15th ; the demonstrations are in ge- neral shorter . Book XI . Def . 10. is retained , as univerfally true , for the reafons given in the ...
... 11. book V. by Mr Simpson . The 5th and 6th propofitions are joined in one , as also the 14th and 15th ; the demonstrations are in ge- neral shorter . Book XI . Def . 10. is retained , as univerfally true , for the reafons given in the ...
Side x
... Book XI . will appear from the following obfervations : He has proved that the triangles EAB , EBC , ECA , contain- ing the one folid , are equal and fimilar to the three triangles FAB , FBC , FCA , containing the other folid , and ...
... Book XI . will appear from the following obfervations : He has proved that the triangles EAB , EBC , ECA , contain- ing the one folid , are equal and fimilar to the three triangles FAB , FBC , FCA , containing the other folid , and ...
Side xi
... Book XI . to fupply its defect . prop . C. " Solid figures contained by the fame num- " ber of equal and fimilar planes alike fituated , and having none " of their folid angles contained by more than three plane angles , are equal and ...
... Book XI . to fupply its defect . prop . C. " Solid figures contained by the fame num- " ber of equal and fimilar planes alike fituated , and having none " of their folid angles contained by more than three plane angles , are equal and ...
Side 1
... BOOK I. DEFINITIONS . A I Point is that which hath no parts or magnitude . II . A line is length without breadth ... XI . An BOOK I. Book I. XI . An obtufe angle is that which THE ...
... BOOK I. DEFINITIONS . A I Point is that which hath no parts or magnitude . II . A line is length without breadth ... XI . An BOOK I. Book I. XI . An obtufe angle is that which THE ...
Side 2
... Book I. XI . An obtufe angle is that which is greater than a right one . XII . An acute angle is that which is less than a right one . XIII . A term , or bound , is the extreme of any thing . XIV . A figure is that which is contained ...
... Book I. XI . An obtufe angle is that which is greater than a right one . XII . An acute angle is that which is less than a right one . XIII . A term , or bound , is the extreme of any thing . XIV . A figure is that which is contained ...
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Vanlige uttrykk og setninger
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Populære avsnitt
Side 93 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides. Let AC, CF be equiangular parallelograms, having the angle BCD equal to the angle ECG ; the...
Side 78 - ... viz. as A is to B, fo is E to F, and B to C as D to E ; and if the firft A be greater than the third C, then the fourth D will be greater than the fixth F ; if equal, equal ; and, if lefs, lefs.
Side 88 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Side 99 - BAC was proved to be equal to ACD : Therefore the whole angle ACE is equal to the two angles ABC, BAC...
Side 19 - From this it is manifest that if one angle of a triangle be equal to the other two it is a right angle, because the angle adjacent to it is equal to the same two ; (i.
Side 75 - Let AB be the fame multiple of C, that DE is of F : C is to F, as AB to DE. Becaufe AB is the fame multiple of C that DE is of F ; there are as many magnitudes in AB equal to C, as there are in DE equal...
Side 88 - ... reciprocally proportional, are equal to one another. Let AB, BC be equal parallelograms which have the angles at B equal, and let the sides DB, BE be placed in the same straight line ; wherefore also FB, BG are in one straight line (2.
Side 99 - BGC: for the same reason, whatever multiple the circumference EN is of the circumference EF, the same multiple is the angle EHN of the angle EHF: and if the circumference BL be equal to the circumference EN, the angle BGL is also equal to the angle EHN ; (in.
Side 106 - ... but BD, BE, which are in that plane, do each of them meet AB ; therefore each of the angles ABD, ABE is a right angle ; for the same reason, each of the angles CDB, CDE is a right angle: and because AB is equal to DE, and BD...
Side 73 - RATIOS that are the same to the same ratio, are the same to one another. Let A be to B as C is to D ; and as C to D, so let E be to F ; A is to B, as E to F.