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 sider |
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Side viii
... reason , because , to mea- sure the length of the simplest of all the curves which Geometry treats of , and the space contained within it , are problems that certainly belong to the elements of the science , especially as they are not ...
... reason , because , to mea- sure the length of the simplest of all the curves which Geometry treats of , and the space contained within it , are problems that certainly belong to the elements of the science , especially as they are not ...
Side xii
... reasons , I would willingly reserve it , or rather a compend of it , for a separate work , intended as an introduction to the study of that analysis . In explaining the elements of Plane and Spherical Trigonometry , xii PREFACE .
... reasons , I would willingly reserve it , or rather a compend of it , for a separate work , intended as an introduction to the study of that analysis . In explaining the elements of Plane and Spherical Trigonometry , xii PREFACE .
Side xv
... reason to account it of no consequence to know what the propositions are , which must cease to be true if this proposition were sup- posed to be false ? Is it not useful to know , that unless it be true , that any two sides of a ...
... reason to account it of no consequence to know what the propositions are , which must cease to be true if this proposition were sup- posed to be false ? Is it not useful to know , that unless it be true , that any two sides of a ...
Side 34
... reason , the exterior angle CEB of the triangle ABE is greater than BAC ; and it has been demonstrated that the angle BDC is greater than the angle CEB ; much more then is the angle BDC greater than the angle BAC . Therefore , if from ...
... reason , the exterior angle CEB of the triangle ABE is greater than BAC ; and it has been demonstrated that the angle BDC is greater than the angle CEB ; much more then is the angle BDC greater than the angle BAC . Therefore , if from ...
Side 44
... reason EF is equal to BC ; wherefore AD is equal ( 1. Ax . ) to EF ; and DE is common ; therefore the whole , or the remainder , AE is equal ( 2. or 3. Ax . ) to the whole , or the remainder DF ; now AB is also equal to DC ; therefore ...
... reason EF is equal to BC ; wherefore AD is equal ( 1. Ax . ) to EF ; and DE is common ; therefore the whole , or the remainder , AE is equal ( 2. or 3. Ax . ) to the whole , or the remainder DF ; now AB is also equal to DC ; therefore ...
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Vanlige uttrykk og setninger
ABC is equal ABCD altitude angle ABC angle ACB angle BAC angle EDF arch AC base BC bisected centre circle ABC circumference common section cosine cylinder demonstrated diameter draw drawn 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 parallelepipeds parallelogram perpendicular polygon prism PROB 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 straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore
Populære avsnitt
Side 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...
Side 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.
Side 33 - THE greater angle of every triangle is subtended by the greater side, or has the greater side opposite to it.
Side 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...
Side 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.
Side 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.
Side 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.
Side 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.
Side 77 - THE straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle...
Side 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.