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 100.
Σελίδα 13
... bases , or third sides , shall be equal ; and the areas of the triangles shall be equal ; and their other angles shall be ... base EF ; and the tri- angle ABC to the triangle DEF ; and the other an- gles , to which the equal sides are ...
... bases , or third sides , shall be equal ; and the areas of the triangles shall be equal ; and their other angles shall be ... base EF ; and the tri- angle ABC to the triangle DEF ; and the other an- gles , to which the equal sides are ...
Σελίδα 14
... base BC shall coincide with the base EF cor . def . 3. ) , and shall be equal to it . Therefore also the whole triangle ABC shall coincide with the whole triangle DEF , so that the spaces which they contain or their areas are equal ...
... base BC shall coincide with the base EF cor . def . 3. ) , and shall be equal to it . Therefore also the whole triangle ABC shall coincide with the whole triangle DEF , so that the spaces which they contain or their areas are equal ...
Σελίδα 15
... base . COROLLARY . Hence every equilateral triangle is also equiangular PROP . VI . THEOR . If two angles of a ... base DC is equal to the base AB , and the area of the triangle DBC is equal to that of the triangle ( 4. 1. ) ACB , the ...
... base . COROLLARY . Hence every equilateral triangle is also equiangular PROP . VI . THEOR . If two angles of a ... base DC is equal to the base AB , and the area of the triangle DBC is equal to that of the triangle ( 4. 1. ) ACB , the ...
Σελίδα 16
... base CD are equal ( 5. 1. ) to one another , but the angle ECD is greater than the angle BCD ; wherefore the angle ... base , and on the same side of it , there cannot be two triangles that have their sides which are terminated in one ...
... base CD are equal ( 5. 1. ) to one another , but the angle ECD is greater than the angle BCD ; wherefore the angle ... base , and on the same side of it , there cannot be two triangles that have their sides which are terminated in one ...
Σελίδα 17
... base EF , and upon the same side of it , there can be two triangles EDF , EGF , that have their sides which are terminated in one extremity of the base equal to one another , and like- wise their sides terminated in the other extremity ...
... base EF , and upon the same side of it , there can be two triangles EDF , EGF , that have their sides which are terminated in one extremity of the base equal to one another , and like- wise their sides terminated in the other extremity ...
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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.