The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh and Twelfth ; the Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected, and Some of Euclid's Demonstrations are Restored ; Also the Book of Euclid's Data, in Like Manner CorrectedDesilver, 1829 - 516 páginas |
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Página 3
... Definitions and Demonstrations as they are in the Greek editions we now have , I found that Theon , or whoever was the editor of the present Greek text , by adding some things , suppress- ing others , and mixing his own with Euclid's ...
... Definitions and Demonstrations as they are in the Greek editions we now have , I found that Theon , or whoever was the editor of the present Greek text , by adding some things , suppress- ing others , and mixing his own with Euclid's ...
Página 4
... Definition which Eudoxus or Euclid had given of compound ratio , and giving an absurd one in place of it , in the 5th Definition of the 6th Book , which neither Euclid , Archimedes , Appollonius , nor any geo- meter before Theon's time ...
... Definition which Eudoxus or Euclid had given of compound ratio , and giving an absurd one in place of it , in the 5th Definition of the 6th Book , which neither Euclid , Archimedes , Appollonius , nor any geo- meter before Theon's time ...
Página 5
... Definition of the 11th Book , which is not a right definition , because there may be solids con- tained by the same number of similar plane figures , which are not similar to one another , in the true sense of simi- larity received by ...
... Definition of the 11th Book , which is not a right definition , because there may be solids con- tained by the same number of similar plane figures , which are not similar to one another , in the true sense of simi- larity received by ...
Página 6
... Definition of Book 11th ; besides , the Translation is much amended by the friendly assistance of a learned ... DEFINITIONS . I. vi PREFACE .
... Definition of Book 11th ; besides , the Translation is much amended by the friendly assistance of a learned ... DEFINITIONS . I. vi PREFACE .
Página 7
... DEFINITIONS . I. A POINT is that which hath no parts , or which hath no mag- nitude . II . III . A line is length without breadth . The extremities of a line are points . IV . A straight line is that which lies evenly between its ...
... DEFINITIONS . I. A POINT is that which hath no parts , or which hath no mag- nitude . II . III . A line is length without breadth . The extremities of a line are points . IV . A straight line is that which lies evenly between its ...
Otras ediciones - Ver todas
The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ... Robert Simson,Euclid Euclid Sin vista previa disponible - 2018 |
Términos y frases comunes
altitude angle ABC angle BAC base BC BC is equal BC is given bisected centre circle ABCD circumference co-sine cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid ex æquali excess fore given angle given in magnitude given in position given in species given magnitude given ratio given straight line gnomon greater join less Let ABC multiple parallel parallelogram parallelogram AC perpendicular point F polygon prism proportionals proposition Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment sides BA similar sine solid angle solid parallelopipeds square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore
Pasajes populares
Página 9 - Let it be granted that a straight line may be drawn from any one point to any other point.
Página 81 - The angles in the same segment of a circle are equal to one another.
Página 315 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Página 33 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Página 49 - If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part.
Página 96 - If from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.
Página 155 - 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.
Página 22 - ANY two angles of a triangle are together less than two right angles.
Página 25 - Let A, B, C be the three given straight lines, of which any two whatever are greater than the third, viz.
Página 24 - Any two sides of a triangle are together greater than the third side.