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 sider |
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Resultat 1-5 av 43
Side 29
... evidently equal to all the interior angles of all the triangles , that is , to twice as many right angles as there are triangles , or twice as many right angles as the figure has sides , wanting the angles of two tri- angles , that is ...
... evidently equal to all the interior angles of all the triangles , that is , to twice as many right angles as there are triangles , or twice as many right angles as the figure has sides , wanting the angles of two tri- angles , that is ...
Side 39
... evidently as many columns as there are parts in AB ; while in each column there are as many squares as there are parts in AD . The number of such squares contained in a figure is called , in the language of mensuration , the area of ...
... evidently as many columns as there are parts in AB ; while in each column there are as many squares as there are parts in AD . The number of such squares contained in a figure is called , in the language of mensuration , the area of ...
Side 44
... evidently rectangles ; and BH is equal ( I. ax . 10 ) to BK , DL , EH . But BH is contained by A and BC , for ( II . def . 1 ) it is contained by GB and BC , and GB is equal ( const . ) to A ; and BK is contained by A and BD , for it is ...
... evidently rectangles ; and BH is equal ( I. ax . 10 ) to BK , DL , EH . But BH is contained by A and BC , for ( II . def . 1 ) it is contained by GB and BC , and GB is equal ( const . ) to A ; and BK is contained by A and BD , for it is ...
Side 59
... evidently perpendicular to chords joining AB and K B * In Simson's edition , the construction commences thus , " Draw within the circle any straight line AB . " This mode of expression is improper , as it is not to be assumed till the ...
... evidently perpendicular to chords joining AB and K B * In Simson's edition , the construction commences thus , " Draw within the circle any straight line AB . " This mode of expression is improper , as it is not to be assumed till the ...
Side 70
... evidently a third case , viz . , when AB or AC passes through the centre : but though this case is not given in a separate form , its proof is contained in that of either of the others . + The demonstration here adopted has the ...
... evidently a third case , viz . , when AB or AC passes through the centre : but though this case is not given in a separate form , its proof is contained in that of either of the others . + The demonstration here adopted has the ...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ... James Thomson, gen,James Euclides Ingen forhåndsvisning tilgjengelig - 2016 |
Vanlige uttrykk og setninger
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
Populære avsnitt
Side 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.
Side 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.
Side 2 - A rhombus is that which has all its sides equal, but its angles are not right angles.
Side 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.
Side 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.
Side 7 - If two triangles have two sides of the one equal to two sides of the...
Side 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.
Side 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.
Side 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.
Side 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.