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 |
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Αποτελέσματα 1 - 5 από τα 100.
Σελίδα 12
... ABC is an equilateral triangle . Because the point A is the cen- tre of the circle BCD , AC is equal C D A B E ( 11. Definition ) to AB ; and because the point B is the centre of the cir- cle ACE , BC is equal to AB : But it has been ...
... ABC is an equilateral triangle . Because the point A is the cen- tre of the circle BCD , AC is equal C D A B E ( 11. Definition ) to AB ; and because the point B is the centre of the cir- cle ACE , BC is equal to AB : But it has been ...
Σελίδα 13
... ABC , DEF be two triangles which have the two sides AB , AC equal to the two sides DE , DF , each to each , viz . AB ... triangle DEF ; and the other an- gles , to which the equal sides are opposite , shall be equal , each to each , A D ΔΔ ...
... ABC , DEF be two triangles which have the two sides AB , AC equal to the two sides DE , DF , each to each , viz . AB ... triangle DEF ; and the other an- gles , to which the equal sides are opposite , shall be equal , each to each , A D ΔΔ ...
Σελίδα 14
... triangle ABC shall coincide with the whole triangle DEF , so that the spaces which they contain or their areas are equal ; and the remaining angles of the one shall coincide with the ... triangle ABC : And it has also 14 ELEMENTS.
... triangle ABC shall coincide with the whole triangle DEF , so that the spaces which they contain or their areas are equal ; and the remaining angles of the one shall coincide with the ... triangle ABC : And it has also 14 ELEMENTS.
Σελίδα 15
... ABC : And it has also been 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 ... triangle be equal to one another , the sides which ...
... ABC : And it has also been 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 ... triangle be equal to one another , the sides which ...
Σελίδα 16
... triangle ACB ; produce AC , AD to E , F ; therefore , because AC is equal to ... ABC , DEF be two triangles having the two sides AB , AC , equal to the two ... triangle ABC be applied to the triangle DEF , so that the point B be ...
... triangle ACB ; produce AC , AD to E , F ; therefore , because AC is equal to ... ABC , DEF be two triangles having the two sides AB , AC , equal to the two ... triangle ABC be applied to the triangle DEF , so that the point B be ...
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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 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.