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 TrigonometryJ.P. Lippincott & Company, 1855 - 318 σελίδες |
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Αποτελέσματα 1 - 5 από τα 67.
Σελίδα 12
... the remainder ( 3 . K H D E G 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.
... the remainder ( 3 . K H D E G 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.
Σελίδα 22
... shewn that B 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 ...
... shewn that B 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 ...
Σελίδα 23
... shewn that BA , AC are greater than BE , EC ; much more then are BA , AC great- er than BD , DC . B A. E D 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 A. E D Again , because the exterior angle of a triangle ( 16. 1. ) is greater than the interior and opposite angle , the exte- rior ...
Σελίδα 25
... angle EDF and it was shewn that it is no equal to it : therefore the angle BAC is greater than the angle EDF . B C E THEOR . PROP . XXVI . If two triangles have 4 OF GEOMETRY . BOOK I. 25 DF; but the angle BAC greater than the angle ...
... angle EDF and it was shewn that it is no equal to it : therefore the angle BAC is greater than the angle EDF . B C E THEOR . PROP . XXVI . If two triangles have 4 OF GEOMETRY . BOOK I. 25 DF; but the angle BAC greater than the angle ...
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 . E PROP . XXXI . PROB . F G B H K D 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 . E PROP . XXXI . PROB . F G B H K D 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 definition 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 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
Δημοφιλή αποσπάσματα
Σελίδα 51 - 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 29 - 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.
Σελίδα 12 - To draw a straight line through a given point parallel to a given straight line. Let A be the given point, and BC the given straight line.
Σελίδα 11 - 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 line. 3. And that a circle may be described from any centre, at any distance from that centre.
Σελίδα 72 - To draw a straight line from a given point, either without or in the circumference, which shall touch a given circle. First, let A be a given point without the given circle BCD : it is required to draw a straight line from A which shall touch the circle.
Σελίδα 84 - If from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.
Σελίδα 80 - 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.
Σελίδα 22 - Any two sides of a triangle are together greater than the third side.
Σελίδα 53 - If a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.
Σελίδα 35 - Parallelograms upon the same base and between the same parallels, are equal to one another.