Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle, and the Geometry of Solids: to which are Added, Elements of Plane and Spherical TrigonometryW. E. Dean, 1847 - 317 σελίδες |
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Αποτελέσματα 1 - 5 από τα 71.
Σελίδα 4
... demonstrating more easily some of the properties of parallel lines . In the third Book , the re- marks concerning the angles made by a straight line , and the circumference of a circle , are left out , as tending to perplex one who has ...
... demonstrating more easily some of the properties of parallel lines . In the third Book , the re- marks concerning the angles made by a straight line , and the circumference of a circle , are left out , as tending to perplex one who has ...
Σελίδα 6
... demonstrate it to others when it has been found out . This is either Analytical or Syn- thetical . 16. Analysis , or the Analytic method , is the art or mode of finding out the truth of a proposition , by first supposing the thing to be ...
... demonstrate it to others when it has been found out . This is either Analytical or Syn- thetical . 16. Analysis , or the Analytic method , is the art or mode of finding out the truth of a proposition , by first supposing the thing to be ...
Σελίδα 14
... demonstrated , that the whole angle ABG is equal to the whole ACF , and the part CBG to the part BCF , the remaining angle ABC is therefore equal to the remaining angle ACB , which are the angles at the base of the triangle ABC : And it ...
... demonstrated , that the whole angle ABG is equal to the whole ACF , and the part CBG to the part BCF , the remaining angle ABC is therefore equal to the remaining angle ACB , which are the angles at the base of the triangle ABC : And it ...
Σελίδα 15
... ; much more then is the angle BDC greater than the angle BCD . Again , because CB is equal to DB , the angle BDC is equal ( 5. 1. ) to the angle BCD ; A C B but it has been demonstrated to be greater than it OF GEOMETRY . BOOK I. 15.
... ; much more then is the angle BDC greater than the angle BCD . Again , because CB is equal to DB , the angle BDC is equal ( 5. 1. ) to the angle BCD ; A C B but it has been demonstrated to be greater than it OF GEOMETRY . BOOK I. 15.
Σελίδα 16
... demonstrated to be greater than it ; which is impossi ble . But if one of the vertices , as D , be within the other triangle ACB ; produce AC , AD to E , F ; therefore , because AC is equal to AD in the triangle ACD , the angles ECD ...
... demonstrated to be greater than it ; which is impossi ble . But if one of the vertices , as D , be within the other triangle ACB ; produce AC , AD to E , F ; therefore , because AC is equal to AD in the triangle ACD , the angles ECD ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC base BC bisected centre chord circle ABC circumference cosine cylinder demonstrated diameter divided draw equal and similar equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given rectilineal given straight line greater Hence hypotenuse inscribed join less Let ABC Let the straight magnitudes meet multiple opposite angle parallel parallelogram parallelopiped perpendicular polygon prism PROB PROP proportional proposition quadrilateral radius ratio rectangle contained rectilineal figure remaining angle right angled triangle SCHOLIUM segment semicircle shewn side BC sine solid angle solid parallelopiped spherical angle spherical triangle square straight line BC THEOR third touches the circle triangle ABC triangle DEF wherefore
Δημοφιλή αποσπάσματα
Σελίδα 53 - If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line.
Σελίδα 18 - If two triangles have two sides of the one equal to two sides of the...
Σελίδα 54 - 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.
Σελίδα 82 - The angle in a semicircle is a right angle; the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle.
Σελίδα 31 - Straight lines which are parallel to the same straight line are parallel to one another. Triangles and Rectilinear Figures. The sum of the angles of a triangle is equal to two right angles.
Σελίδα 11 - 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.
Σελίδα 21 - The angles which one straight line makes with another upon one side of it, are either two right angles, or are together equal to two right angles. Let the straight line AB make with CD, upon one side of it, the angles CBA, ABD : these shall either be two right angles, or shall together be equal to two right angles. For...
Σελίδα 101 - To describe an isosceles triangle, having each of the angles at the base double of the third angle.
Σελίδα 58 - AB into two parts, so that the rectangle contained by the whole line and one of the parts, shall be equal to the square on the other part.
Σελίδα 298 - 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.