Elements of Geometry: Containing the First Six Books of Euclid: With a Supplement on the Quadrature of the Circle and the Geometry of Solids ...J. Eastburn & Company, 1819 - 317 páginas |
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Página vii
... third Book , the remarks con- cerning the angles made by a straight line , and the circumference of a circle , are left out , as tending to perplex one who has advanced no farther than the ele- ments of the science . The 27th , 28th ...
... third Book , the remarks con- cerning the angles made by a straight line , and the circumference of a circle , are left out , as tending to perplex one who has advanced no farther than the ele- ments of the science . The 27th , 28th ...
Página ix
... Third Book , I have departed from EUCLID altogether , with a view of rendering it both shorter and more comprehensive . This , however , is not attempted b B introducing a mode of reasoning less rigorous than that of PREFACE . ix.
... Third Book , I have departed from EUCLID altogether , with a view of rendering it both shorter and more comprehensive . This , however , is not attempted b B introducing a mode of reasoning less rigorous than that of PREFACE . ix.
Página xv
... third ; it may be replied , that this is no doubt a truth , which , without proof , most inen will be inclined to admit ; but are we for that reason to account it of no consequence to know what the propositions are , which must cease to ...
... third ; it may be replied , that this is no doubt a truth , which , without proof , most inen will be inclined to admit ; but are we for that reason to account it of no consequence to know what the propositions are , which must cease to ...
Página 23
... third sides , shall be equal ; and the areas of the triangles shall be equal ; and their other angles shall be equal , each to each , viz . those to which the equal sides are opposite * . Let ABC , DEF be two triangles which have the ...
... third sides , shall be equal ; and the areas of the triangles shall be equal ; and their other angles shall be equal , each to each , viz . those to which the equal sides are opposite * . Let ABC , DEF be two triangles which have the ...
Página 33
... third side . Let ABC be a triangle ; any two sides of it together are greater than the third side , viz . the sides BA , AC greater than the side BC ; and AB , BC greater than AC ; and BC , CA greater than AB . Produce BA to the point D ...
... third side . Let ABC be a triangle ; any two sides of it together are greater than the third side , viz . the sides BA , AC greater than the side BC ; and AB , BC greater than AC ; and BC , CA greater than AB . Produce BA to the point D ...
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Términos y frases comunes
ABC is equal ABCD altitude angle ABC angle ACB angle BAC arch AC base BC bisected centre circle ABC circumference common section cosine cylinder demonstrated diameter draw equal and similar equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater hypotenuse inscribed join less Let ABC Let the straight line BC magnitudes meet opposite angle parallel parallelogram perpendicular polygon prism produced proportionals proposition Q. E. D. COR Q. E. D. PROP radius ratio rectangle contained rectilineal figure remaining angle segment semicircle shewn side BC sine solid angle solid parallelepipeds spherical angle spherical triangle SPHERICAL TRIGONOMETRY straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore
Pasajes populares
Página 153 - If from the vertical angle of a triangle a straight line be drawn perpendicular to the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the perpendicular and the diameter of the circle...
Página 19 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.
Página 33 - THE greater angle of every triangle is subtended by the greater side, or has the greater side opposite to it.
Página 292 - If a straight line meet two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...
Página 308 - 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 36 - IF two triangles have two sides of the one equal to two sides of the other, each to each, but the angle contained by the two sides of one of them greater than the angle contained by the two sides equal to them, of the other ; the base of that which has the greater angle shall be greater than the base of the other.
Página 18 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it.
Página 78 - To draw a straight line from a given point, either without or in the circumference, which shall touch a given circle. First, let A be a given point without the given circle BCD : it is required to draw a straight line from A which shall touch the circle.
Página 77 - THE straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle...
Página 39 - If a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another ; and the exterior angle equal to the interior and opposite upon the same side ; and likewise the too interior angles upon the same side together equal to two right angles.