The Elements of Euclid; viz. the first six books,together with the eleventh and twelfth, with an appendixThomas Tegg, 1841 - 351 páginas |
Dentro del libro
Resultados 1-5 de 100
Página 9
... greater . It is required to cut off from AB , the greater , a part equal to C , the less . T E B * 2. 1 . From the point A draw✶ the straight line AD equal to C ; and from the centre A , and at the distance AD , describe the circle DEF ...
... greater . It is required to cut off from AB , the greater , a part equal to C , the less . T E B * 2. 1 . From the point A draw✶ the straight line AD equal to C ; and from the centre A , and at the distance AD , describe the circle DEF ...
Página 13
... greater , which is absurd . Therefore AB is not unequal to AC , that is , it is equal to it . Wherefore , if two ... greater than the angle BCD ; therefore the angle ADC is also greater than the angle BCD ; much more then is the angle ...
... greater , which is absurd . Therefore AB is not unequal to AC , that is , it is equal to it . Wherefore , if two ... greater than the angle BCD ; therefore the angle ADC is also greater than the angle BCD ; much more then is the angle ...
Página 21
... greater than the angle ECF ; therefore the angle ACD is greater than BAE . In like manner , if the side BC be bisected , and AC be produced to G , it may be demonstrated that the angle BCG , that is , * * 15. 1 . the angle ACD , is greater ...
... greater than the angle ECF ; therefore the angle ACD is greater than BAE . In like manner , if the side BC be bisected , and AC be produced to G , it may be demonstrated that the angle BCG , that is , * * 15. 1 . the angle ACD , is greater ...
Página 22
... greater than the angles 13. 1. ABC , ACB ; but ACD , ACB are together equal to two right angles ; therefore the ... greater side of every triangle is opposite to the greater angle . Let ABC be a triangle , of which the side AC is greater ...
... greater than the angles 13. 1. ABC , ACB ; but ACD , ACB are together equal to two right angles ; therefore the ... greater side of every triangle is opposite to the greater angle . Let ABC be a triangle , of which the side AC is greater ...
Página 23
Euclides William Rutherford. greater than the angle BCA ; the side AC shall be greater than the side AB . For , if it be not greater , AC must either be equal to AB , or less than it ; it is not equal , because then the angle ABC would ...
Euclides William Rutherford. greater than the angle BCA ; the side AC shall be greater than the side AB . For , if it be not greater , AC must either be equal to AB , or less than it ; it is not equal , because then the angle ABC would ...
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.