The Elements of Euclid; viz. the first six books,together with the eleventh and twelfth, with an appendixThomas Tegg, 1841 - 351 páginas |
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Página 14
... Q. E. D. PROP . VIII . THEOR . If two triangles have two sides of the one equal to two sides of the other , each to each , and have likewise their bases equal ; the angle which is contained by the two sides of the one shall be equal to ...
... Q. E. D. PROP . VIII . THEOR . If two triangles have two sides of the one equal to two sides of the other , each to each , and have likewise their bases equal ; the angle which is contained by the two sides of the one shall be equal to ...
Página 15
... Q. E. D. PROP . IX . PROB . To bisect a given rectilineal angle , that is , to divide it into two equal angles . Let BAC be the given rectilineal angle , it is re- quired to bisect it . A Take any point D in AB , and from AC cut off ...
... Q. E. D. PROP . IX . PROB . To bisect a given rectilineal angle , that is , to divide it into two equal angles . Let BAC be the given rectilineal angle , it is re- quired to bisect it . A Take any point D in AB , and from AC cut off ...
Página 19
... Q. E. D. PROP . XIV . THEOR . If , at a point in a straight line , two other straight lines , upon the opposite sides of it , make the adjacent angles together equal to two right angles , these two straight lines shall be in one and the ...
... Q. E. D. PROP . XIV . THEOR . If , at a point in a straight line , two other straight lines , upon the opposite sides of it , make the adjacent angles together equal to two right angles , these two straight lines shall be in one and the ...
Página 20
... Q. E. D. PROP . XV . THEOR . If two straight lines cut one another , the vertical , or opposite , angles shall be equal . Let the two straight lines AB , CD cut one another in the point E ; the angle AEC shall be equal to the angle DEB ...
... Q. E. D. PROP . XV . THEOR . If two straight lines cut one another , the vertical , or opposite , angles shall be equal . Let the two straight lines AB , CD cut one another in the point E ; the angle AEC shall be equal to the angle DEB ...
Página 21
... Q. E. D. PROP . XVII . THEOR . Any two angles of a triangle are together less than two right angles . Let ABC be any triangle ; any two of its angles to- gether shall be less than two right angles . Produce BC to D ; and be- cause ACD ...
... Q. E. D. PROP . XVII . THEOR . Any two angles of a triangle are together less than two right angles . Let ABC be any triangle ; any two of its angles to- gether shall be less than two right angles . Produce BC to D ; and be- cause ACD ...
Otras ediciones - Ver todas
The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Euclid Sin vista previa disponible - 2015 |
The Elements of Euclid: Viz. the First Six Books, Together With the Eleventh ... Euclid Sin vista previa disponible - 2023 |
Términos y frases comunes
AB is equal AC is equal altitude angle ABC angle ACB angle BAC base BC bisect centre circle ABCD circle EFGH circumference common section cone cylinder demonstrated described diameter draw equal to F equiangular equilateral equimultiples exterior angle fore given rectilineal given straight line gnomon inscribed join less Let ABC meet multiple opposite angle parallel parallelogram parallelopiped perpendicular polygon prisms PROB proved pyramid ABCG pyramid DEFH Q. E. D. PROP rectangle contained rectilineal figure remaining angle right angles segment solid angle solid CD sphere square of AC straight line AC THEOR third three plane angles three straight lines tiples touches the circle triangle ABC triangle DEF triplicate ratio twice the rectangle wherefore whole
Pasajes populares
Página 173 - 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.
Página 56 - Iff 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.
Página 53 - 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 on the line between the points of section, is equal to the square on half the line.
Página 58 - IF a straight line be divided into two equal, and also into two unequal parts; the squares of the two unequal parts are together double of the square of half the line, and of the square of the line between the points of section.
Página 94 - 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.
Página 23 - Any two sides of a triangle are together greater than the third side.
Página 40 - EQUAL triangles upon the same base, and upon the same side of it, are between the same parallels.
Página 103 - 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 on the line which touches it.
Página 50 - PROP. I. THEOR. If there oe two straight lines, one of which is divided into any number of parts; the rectangle contained by the two straight lines, is equal to the rectangles contained by the undivided line, and the several parts of the divided line.
Página 28 - If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent.