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 sider |
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Resultat 1-5 av 93
Side 11
... produced ever so far both ways , do not meet . POSTULATES . 1. LET it be granted that a straight line may be drawn from any one point to any other point . 2. That a terminated straight line may be produced to any length in a straight ...
... produced ever so far both ways , do not meet . POSTULATES . 1. LET it be granted that a straight line may be drawn from any one point to any other point . 2. That a terminated straight line may be produced to any length in a straight ...
Side 12
... produce ( 2. Post . ) the straight lines DA , BD , to E and F ; from the centre B , at the distance BC , describe ( 3. Post . ) the circle CGH , and from the centre D , at the dis- tance DG , describe the circle GKL , AL is equal to BC ...
... produce ( 2. Post . ) the straight lines DA , BD , to E and F ; from the centre B , at the distance BC , describe ( 3. Post . ) the circle CGH , and from the centre D , at the dis- tance DG , describe the circle GKL , AL is equal to BC ...
Side 14
... produced , the angles upon the other side of the base shall be equal . Let ABC be an isosceles triangle , of which the side AB is equal to AC , and let the straight lines AB , AC be produced to D and E , the angle ABC shall be equal to ...
... produced , the angles upon the other side of the base shall be equal . Let ABC be an isosceles triangle , of which the side AB is equal to AC , and let the straight lines AB , AC be produced to D and E , the angle ABC shall be equal to ...
Side 16
... produce AC , AD to E , F ; therefore , because AC is equal to AD in the triangle ACD , the angles ECD , FDC upon the other side of the base CD are equal ( 5. 1. ) to one another , but the angle ECD is greater than the angle BCD ...
... produce AC , AD to E , F ; therefore , because AC is equal to AD in the triangle ACD , the angles ECD , FDC upon the other side of the base CD are equal ( 5. 1. ) to one another , but the angle ECD is greater than the angle BCD ...
Side 18
... produced to any length both ways , and let C be a point without it . It is required to draw a straight . line perpendicular to AB from the point C. C Take any point D upon the other side of AB , and from the centre C , at the distance ...
... produced to any length both ways , and let C be a point without it . It is required to draw a straight . line perpendicular to AB from the point C. C Take any point D upon the other side of AB , and from the centre C , at the distance ...
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Elements of Geometry: Containing the First Six Books of Euclid: With a ... John Playfair Uten tilgangsbegrensning - 1854 |
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 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
Populære avsnitt
Side 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.
Side 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.
Side 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.
Side 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.
Side 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.
Side 33 - Parallelograms upon the same base and between the same parallels, are equal to one another.
Side 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...
Side 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.
Side 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.
Side 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.