Euclid's Elements [book 1-6] with corrections, by J.R. Young1838 |
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Página 88
... circles , & c . Q.E.D. PROP . XIII . THEOR . One circle cannot touch another in more points than one , whether it touches it on the inside or on the outside . For , if it be possible , let the circle EBF touch the circle ABC in more ...
... circles , & c . Q.E.D. PROP . XIII . THEOR . One circle cannot touch another in more points than one , whether it touches it on the inside or on the outside . For , if it be possible , let the circle EBF touch the circle ABC in more ...
Página 92
... circle , as AC ; and draw DC to the point C , where it meets the circumfer- ence . And because DA is equalt to DC ... touches it only in one point , because , if it did meet the circle in two , it would fall within it . Also , it * 2 . 3 ...
... circle , as AC ; and draw DC to the point C , where it meets the circumfer- ence . And because DA is equalt to DC ... touches it only in one point , because , if it did meet the circle in two , it would fall within it . Also , it * 2 . 3 ...
Página 93
... 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 . * 1 . 3 . # 11 . 1 Find the centre E of the circle , and draw AE cutting the ...
... 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 . * 1 . 3 . # 11 . 1 Find the centre E of the circle , and draw AE cutting the ...
Página 95
... circle , and from the point of contact a straight line be drawn at right angles to the touching line , the centre of ... touches the circle ABC , and FC is drawn from the centre to the point of contact , FC is per- B pendicular to DE ...
... circle , and from the point of contact a straight line be drawn at right angles to the touching line , the centre of ... touches the circle ABC , and FC is drawn from the centre to the point of contact , FC is per- B pendicular to DE ...
Página 106
... touches a circle , and from the point of con- tact a straight line be drawn , cutting the circle , the angles which this line makes with the line touching the circle shall be equal to the angles which are in the alter- nate segments of the ...
... touches a circle , and from the point of con- tact a straight line be drawn , cutting the circle , the angles which this line makes with the line touching the circle shall be equal to the angles which are in the alter- nate segments of the ...
Otras ediciones - Ver todas
Euclid's Elements [Book 1-6] With Corrections, by J.R. Young Euclides Sin vista previa disponible - 2023 |
Euclid's Elements [Book 1-6] with Corrections, by J.R. Young Euclides Sin vista previa disponible - 2018 |
Euclid's Elements [Book 1-6] with Corrections, by J.R. Young Euclides Sin vista previa disponible - 2015 |
Términos y frases comunes
ABCD adjacent angles alternate angles angle ABC angle ACB angle BAC angle BCD angle EDF angles equal antecedent arc BC base BC BC is equal bisected centre circle ABC circumference consequent Const demonstrated described diameter double draw equal angles equal to AC equiangular equilateral and equiangular equimultiples Euclid exterior angle fore Geometry given circle given straight line gnomon greater inscribed join less Let ABC Let the straight logarithm multiple opposite angle parallel parallelogram pentagon perpendicular PROB proportion proposition Q. E. D. PROP radius rectangle contained rectilineal figure remaining angle segment side BC similar sine square of AC straight line AB straight line AC tangent THEOR touches the circle triangle ABC triangle DEF twice the rectangle wherefore
Pasajes populares
Página 30 - IF two triangles have two sides of the one equal to two sides of the other, each to each, but the angle contained by the two sides of one of them greater than the angle contained by the two sides equal to them, of the other ; the base of that which has the greater angle shall be greater than the base of the other.
Página 105 - 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 50 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Página 61 - 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 65 - 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.
Página 70 - To divide a given straight line into two parts, so that the rectangle contained by the whole, and one of the parts, may be equal to the square of the other part.
Página 41 - 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.
Página 172 - 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 45 - TRIANGLES upon the same base, and between the same parallels, are equal to one another.
Página 38 - If a, straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another; and the exterior angle equal to the interior and opposite upon the same side; and likewise the two interior angles upon the same side together equal to two right angles.