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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Side viii
... inscribed in a triangle , and if another triangle be formed by joining the points of contact , each angle of the latter triangle is equal to half the sum of the two angles of the original triangle at the extremities of the side on which ...
... inscribed in a triangle , and if another triangle be formed by joining the points of contact , each angle of the latter triangle is equal to half the sum of the two angles of the original triangle at the extremities of the side on which ...
Side 81
... inscribed in the exterior , and the ex- terior to be circumscribed , or described , about the interior one . 2. When all the angular points of a rectilineal figure are upon the circumference of a circle , the rectilineal figure is said ...
... inscribed in the exterior , and the ex- terior to be circumscribed , or described , about the interior one . 2. When all the angular points of a rectilineal figure are upon the circumference of a circle , the rectilineal figure is said ...
Side 82
... inscribe a triangle equiangular to a given triangle . Let ABC be a given circle , and DEF a given triangle ; it is ... inscribed ( IV . def . 2 ) in the circle ABC : which was to be done . PROP . III . PROB . - About a given circle to ...
... inscribe a triangle equiangular to a given triangle . Let ABC be a given circle , and DEF a given triangle ; it is ... inscribed ( IV . def . 2 ) in the circle ABC : which was to be done . PROP . III . PROB . - About a given circle to ...
Side 83
... inscribed ( IV . def . 3 ) in the triangle ABC ; which was to be done . E B F D Schol . This proposition is a case of the general problem , to describe a circle touching three given straight lines which do not pass through the same ...
... inscribed ( IV . def . 3 ) in the triangle ABC ; which was to be done . E B F D Schol . This proposition is a case of the general problem , to describe a circle touching three given straight lines which do not pass through the same ...
Side 84
... inscribed circle . Hence , in a right- angled triangle the diameter of the inscribed circle is equal to the excess of the sum of the legs above the hypotenuse . It would appear , in like manner , that the diameter of the circle touching ...
... inscribed circle . Hence , in a right- angled triangle the diameter of the inscribed circle is equal to the excess of the sum of the legs above the hypotenuse . It would appear , in like manner , that the diameter of the circle touching ...
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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.