Elements of Geometry: Containing Books 1. to Vi. and Portions of Books Xi. and Xii. of Euclid with Exercises and NotesRivingtons, 1879 - 349 páginas Copy owned by Florence Exton, principle of the college from 1920-1923, when she died unexpectedly in office. |
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Página 3
... common to both lines , CO is said to make with DE the angles COD , COE ; and these ( as having one arm , CO , common to both ) are called adjacent angles . Lastly , if the lines FG , HK cut each other in the point 0 , the lines make ...
... common to both lines , CO is said to make with DE the angles COD , COE ; and these ( as having one arm , CO , common to both ) are called adjacent angles . Lastly , if the lines FG , HK cut each other in the point 0 , the lines make ...
Página 4
... common to all , the angle formed by one of them , OD , D A with OA may be regarded as being made up of the angles AOB , BOC , COD ; that is , we may speak of the angle AOD as a whole , of which the parts are the angles AOB , BOC , and ...
... common to all , the angle formed by one of them , OD , D A with OA may be regarded as being made up of the angles AOB , BOC , COD ; that is , we may speak of the angle AOD as a whole , of which the parts are the angles AOB , BOC , and ...
Página 7
... till he has reached the 17th Proposition of Book I. Euclid next enumerates , as statements of fact , nine Axi or , as he calls them , Common Notions , Book I. ] 7 POSTULATES . EUCLID'S PROPOSITIONS XVIII, TO XXIIJ PROPOSITION D.
... till he has reached the 17th Proposition of Book I. Euclid next enumerates , as statements of fact , nine Axi or , as he calls them , Common Notions , Book I. ] 7 POSTULATES . EUCLID'S PROPOSITIONS XVIII, TO XXIIJ PROPOSITION D.
Página 8
... Common Notions , applicable ( with the exception of the eighth ) to all kinds of magnitudes , and not necessarily ... Common Notions Euclid takes the ground of authority , saying in effect , " To my Postulates I request , to my Common ...
... Common Notions , applicable ( with the exception of the eighth ) to all kinds of magnitudes , and not necessarily ... Common Notions Euclid takes the ground of authority , saying in effect , " To my Postulates I request , to my Common ...
Página 17
... common to BA and CA. .. DE will coincide with and .. is equal to AB , and DF . and EDF . and A DEF . AC , L BAC , △ ABC ; and .. the triangles are equal in all respects . Q. E. D. COR . Hence , -by a process like that in Prop . A , we ...
... common to BA and CA. .. DE will coincide with and .. is equal to AB , and DF . and EDF . and A DEF . AC , L BAC , △ ABC ; and .. the triangles are equal in all respects . Q. E. D. COR . Hence , -by a process like that in Prop . A , we ...
Otras ediciones - Ver todas
Elements of Geometry, Containing Books I. to VI. and Portions of Books XI ... Euclid Vista completa - 1879 |
Elements of Geometry: Containing Books I to VI and Portions of Books XI and ... Thomas Kirkland,J Hamblin 1829-1901 Smith Sin vista previa disponible - 2015 |
Elements of Geometry Containing Books I to VI and Portions of Books XI and ... J. Hamblin Smith,Thos Kirkland Sin vista previa disponible - 2018 |
Términos y frases comunes
AB=DE ABCD AC=DF angle contained angles equal angular points base BC BC=EF centre chord circumference coincide described diagonals diameter divided equal angles equiangular equilateral triangle equimultiples Eucl Euclid exterior angle given circle given line given point given st given straight line greater Hence hypotenuse inscribed intersect isosceles triangle less Let ABC Let the st lines be drawn magnitudes middle points multiple opposite angles opposite sides parallel parallelogram pentagon perpendicular plane polygon produced Prop prove Q. E. D. Ex Q. E. D. PROPOSITION quadrilateral radius ratio rectangle contained reflex angle rhombus right angles segment shew shewn square subtended sum of sqq Take any pt tangent THEOREM together=two rt trapezium triangle ABC triangle be equal vertex vertical angle
Pasajes populares
Página 51 - 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 176 - 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 40 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...
Página 104 - 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 ; it is required to draw a straight line through the point A, parallel to the straight hue BC.
Página 45 - IF a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another...
Página 88 - In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square on the side subtending the obtuse angle, is greater than the squares on the sides containing the obtuse angle, by twice the rectangle contained by the side upon which, when produced, the perpendicular falls, and the straight line intercepted without the triangle between the perpendicular and the obtuse angle, Let ABC be an obtuse-angled triangle, having the obtuse angle...
Página 89 - In every triangle, the square on the side subtending either of the acute angles, is less than the squares on the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the acute angle and the perpendicular let fall upon it from the opposite angle, Let ABC be any triangle, and the angle at B one of its acute angles, and upon BC, one of the sides containing it, let fall the perpendicular AD from the opposite angle.
Página 5 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.
Página 42 - 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 87 - To divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts, shall be equal to the square of the other part.