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 sider |
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Resultat 1-5 av 64
Side 5
... prove the truth of it ; but is received and assented to as soon as mentioned . Such as , the whole of any thing is greater ... proved . Thus , when it is said that the sum of the three angles of any plane tri- angle is equal to two right ...
... prove the truth of it ; but is received and assented to as soon as mentioned . Such as , the whole of any thing is greater ... proved . Thus , when it is said that the sum of the three angles of any plane tri- angle is equal to two right ...
Side 6
... proving that some absurdity would necessarily follow if the proposition advanced were false . This is sometimes called Reductio ad Absurdum ; because it shows the absurdity and falsehood of all suppositions contrary to that contained in ...
... proving that some absurdity would necessarily follow if the proposition advanced were false . This is sometimes called Reductio ad Absurdum ; because it shows the absurdity and falsehood of all suppositions contrary to that contained in ...
Side 12
... proved that CA is equal to AB ; therefore CA , CB are each of them equal to AB ; now things which are equal to the same are equal to one another , ( 1. Axiom ) ; there- fore CA is equal to CB ; wherefore CA , AB , CB are equal to one ...
... proved that CA is equal to AB ; therefore CA , CB are each of them equal to AB ; now things which are equal to the same are equal to one another , ( 1. Axiom ) ; there- fore CA is equal to CB ; wherefore CA , AB , CB are equal to one ...
Side 14
... proved to be equal to GB , therefore the two sides BF , FC are equal to the two CG , GB , each to each ; but the angle BFC is equal to the angle CGB ; wherefore the tri- angles BFC , CGB are equal ( 4. 1. ) , and their remaining angles ...
... proved to be equal to GB , therefore the two sides BF , FC are equal to the two CG , GB , each to each ; but the angle BFC is equal to the angle CGB ; wherefore the tri- angles BFC , CGB are equal ( 4. 1. ) , and their remaining angles ...
Side 15
... proved that the angle FBC is equal to the angle GCB , which are the angles upon the other side of the base . COROLLARY . Hence every equilateral triangle is also equiangular . PROP . VI . THEOR . If two angles of a triangle be equal to ...
... proved that the angle FBC is equal to the angle GCB , which are the angles upon the other side of the base . COROLLARY . Hence every equilateral triangle is also equiangular . PROP . VI . THEOR . If two angles of a triangle be equal to ...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ... John Playfair Uten tilgangsbegrensning - 1839 |
Elements of Geometry: Containing the First Six Books of Euclid with a ... John Playfair Uten tilgangsbegrensning - 1856 |
Vanlige uttrykk og setninger
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 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 touches the circle triangle ABC triangle DEF wherefore
Populære avsnitt
Side 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.
Side 18 - If two triangles have two sides of the one equal to two sides of the...
Side 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.
Side 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.
Side 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.
Side 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.
Side 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...
Side 101 - To describe an isosceles triangle, having each of the angles at the base double of the third angle.
Side 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.
Side 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.