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, 1846 - 317 σελίδες |
Αναζήτηση στο βιβλίο
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 D F E base of the triangle ABC ...
... 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 D F E base of the triangle ABC ...
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 ; C B 2 but it has been demonstrated to be greater than 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 ; C B 2 but it has been demonstrated to be greater than OF GEOMETRY . BOOK I. 15.
Σελίδα 16
... demonstrated to be greater than it ; which is impossi- ble . E F C 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 ...
... demonstrated to be greater than it ; which is impossi- ble . E F C 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 ...
Άλλες εκδόσεις - Προβολή όλων
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 described 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 magnitudes meet multiple opposite angle parallel parallelogram parallelopiped perpendicular plane 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 49 - 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 147 - ... cuts the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight line which bisects the angle.
Σελίδα 292 - 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.
Σελίδα 7 - 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 139 - K hag to M the ratio which is compounded of the ratios of the sides ; therefore also the parallelogram AC has to the parallelogram CF the ratio which is compounded of the ratios of the sides. COR. Hence, any two rectangles are to each other as the products of their bases multiplied by their altitudes.
Σελίδα 33 - Parallelograms upon the same base and between the same parallels, are equal to one another.
Σελίδα 79 - If a straight line touch a circle, and from the point of contact a straight line be drawn cutting the circle, the angles made by...
Σελίδα 125 - 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.
Σελίδα 131 - If four straight lines be proportionals, the rectangle contained by the extremes is equal to the rectangle contained by the means; And if the rectangle contained by the extremes be equal to the rectangle contained by the means, the four straight lines are proportionals. Let the four straight lines, AB, CD, E, F, be proportionals, viz.
Σελίδα 78 - 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.