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 70.
Σελίδα 12
... the remainder ( 3 . K H D E F Ax . ) BG : But it has been shewn that BC is equal to BG ; wherefore AL and BC are each of them equal to BG ; and things that are equal to the same are equal to one another ; therefore 12 ELEMENTS 17.
... the remainder ( 3 . K H D E F Ax . ) BG : But it has been shewn that BC is equal to BG ; wherefore AL and BC are each of them equal to BG ; and things that are equal to the same are equal to one another ; therefore 12 ELEMENTS 17.
Σελίδα 22
... shewn that A it is not equal to AB ; therefore AC is greater than AB . PROP . XX . THEOR . Any two sides of a triangle are together greater than the third side . Let ABC be a triangle ; any two sides of it together are greater than the ...
... shewn that A it is not equal to AB ; therefore AC is greater than AB . PROP . XX . THEOR . Any two sides of a triangle are together greater than the third side . Let ABC be a triangle ; any two sides of it together are greater than the ...
Σελίδα 23
... shewn that BA , AC are greater than BE , EC ; much more then are BA , AC great , er than BD , DC . B D A E Again , because the exterior angle of a triangle ( 16. 1. ) is greater than the interior and opposite angle , the exte- rior ...
... shewn that BA , AC are greater than BE , EC ; much more then are BA , AC great , er than BD , DC . B D A E Again , because the exterior angle of a triangle ( 16. 1. ) is greater than the interior and opposite angle , the exte- rior ...
Σελίδα 25
... an- gle BAC is not less than the angle EDF : and it was shewn that it is not equal to it : therefore the angle BAC is greater than the angle EDF . B AA E PROP . XXVI . THEOR . If two triangles have OF GEOMETRY . BOOK I. 25.
... an- gle BAC is not less than the angle EDF : and it was shewn that it is not equal to it : therefore the angle BAC is greater than the angle EDF . B AA E PROP . XXVI . THEOR . If two triangles have OF GEOMETRY . BOOK I. 25.
Σελίδα 29
... shewn that the angle AGK is equal to the angle GHF ; therefore also AGK is equal to GKD ; and they are alter- nate angles ; therefore AB is parallel C ( 27. 1. ) to CD . G B E H F K D PROP . XXXI . PROB . To draw a straight line through ...
... shewn that the angle AGK is equal to the angle GHF ; therefore also AGK is equal to GKD ; and they are alter- nate angles ; therefore AB is parallel C ( 27. 1. ) to CD . G B E H F K D PROP . XXXI . PROB . To draw a straight line through ...
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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.