The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With the Elements of Plane Trigonometry, and an Appendix in Four Books : With Notes and IllustrationsLongmans, Green, 1845 - 352 páginas |
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Página 10
... reason . When a proposition is demonstrated by supposing one figure to be applied to another , it is said to be proved by the method of superposition . 1 are equal to one another ; for the lines which 10 [ BOOK I. THE ELEMENTS Prove the ...
... reason . When a proposition is demonstrated by supposing one figure to be applied to another , it is said to be proved by the method of superposition . 1 are equal to one another ; for the lines which 10 [ BOOK I. THE ELEMENTS Prove the ...
Página 12
... reason . In other respects this proof is perfectly satisfactory ; and on account of its ease and simplicity , it may perhaps be preferred by those who are reading the Elements for the first time . This proposition may also be proved by ...
... reason . In other respects this proof is perfectly satisfactory ; and on account of its ease and simplicity , it may perhaps be preferred by those who are reading the Elements for the first time . This proposition may also be proved by ...
Página 21
... reason , the exterior angle CEB of the triangle ABE is greater than BAC ; and it has been demon- strated that the angle BDC is greater than CEB : much more then is the angle BDC greater than BAC . Therefore , if from a point , & c . A ...
... reason , the exterior angle CEB of the triangle ABE is greater than BAC ; and it has been demon- strated that the angle BDC is greater than CEB : much more then is the angle BDC greater than BAC . Therefore , if from a point , & c . A ...
Página 33
... reason , the parallelogram EG is equal to the same parallelogram EBCH ; because they are on the same base EH , and between the same parallels EH , BG . There- fore also the parallelogram AC is equal ( I. ax . 1 ) to EG . Where- fore ...
... reason , the parallelogram EG is equal to the same parallelogram EBCH ; because they are on the same base EH , and between the same parallels EH , BG . There- fore also the parallelogram AC is equal ( I. ax . 1 ) to EG . Where- fore ...
Página 37
... reason , the triangles KGC , KFC are equal . Then , because the triangle AEK is equal to AHK , and KGC to KFC , the triangles AEK , KGC are together equal ( I. ax . 2 ) to the triangles AHK , KFC taken together . But the whole triangle ...
... reason , the triangles KGC , KFC are equal . Then , because the triangle AEK is equal to AHK , and KGC to KFC , the triangles AEK , KGC are together equal ( I. ax . 2 ) to the triangles AHK , KFC taken together . But the whole triangle ...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ... James Thomson, gen,James Euclides Sin vista previa disponible - 2016 |
Términos y frases comunes
ABCD altitude angle ABC angle BAC angle equal BC is equal bisected centre chord circle ABC circumference cone const contained corollary cylinder describe a circle diagonal diameter divided draw equal angles equal to AC equiangular equilateral Euclid exterior angle fore fourth given circle given point given ratio given straight line greater half Hence hypotenuse inscribed join less Let ABC magnitudes manner multiple opposite parallel parallelepiped parallelogram perpendicular polygon polyhedron prism PROB.-To produced PROP proportional proposition pyramid radius rectangle rectilineal figure right angles Schol scholium segments semicircle sides similar solid angles square of AC straight line drawn tangent THEOR.-If third triangle ABC trigonometry triplicate ratio vertex vertical angle wherefore
Pasajes populares
Página 130 - 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 45 - If a straight line be bisected, and produced to any point, the rectangle contained by the whole line thus produced, and the part of it produced, together with the square on half the line bisected, is equal to the square on the straight line which is made up of the half and the part produced.
Página 2 - A rhombus is that which has all its sides equal, but its angles are not right angles.
Página 50 - To divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts may be equal to the square on the other part.
Página 38 - In any right-angled triangle, the square which is described upon the side subtending the right angle, is equal to the squares described upon the sides which contain the right angle.
Página 7 - If two triangles have two sides of the one equal to two sides of the...
Página 27 - 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 27 - If a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles ; and the three interior angles of every triangle are equal to two right angles.
Página 15 - If, at a point in a straight line, two other straight lines, upon the opposite sides of it, make the adjacent angles together equal to two right angles, these two straight lines shall be in one and the same straight line.
Página 36 - To describe a parallelogram equal to a given rectilineal figure, and having an angle equal to a given rectilineal angle. Let ABCD be the given rectilineal figure, and E the given rectilineal angle. It is required to describe a parallelogram equal to ABCD, and having an angle equal to E.