# The Elements of Plane Geometry:pPart I(corresponding to Euclid Books I.-II.): Books III.-VI

W.S. Sonnenschein, 1888
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### Ресйечьменб

 The Circle 9 Fundamental Propositions of Proportion 105 Of Ratio and Proportion 109 Fundamental Geometrical Propositions 117
 Definitions 125 Proportion 151 Areas 169 Definitions 197

### ДзмпцйлЮ брпурЬумбфб

УелЯдб 167 - 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.
УелЯдб 9 - 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.
УелЯдб 169 - If four straight lines be proportionals, the rectangle contained by the extremes is equal to the rectangle contained by the means...
УелЯдб 30 - In the same circle, or in equal circles, equal chords are equally distant from the centre ; and of two unequal chords, the less is at the greater distance from the centre.
УелЯдб 171 - ... are to one another in the duplicate ratio of their homologous sides.
УелЯдб 150 - Four quantities are in proportion when the ratio of the first to the second is equal to the ratio of the third to the fourth.
УелЯдб 115 - IF any number of magnitudes be proportionals, as one of the antecedents is to its consequent, so shall all the antecedents taken together be to all the consequents. Let...
УелЯдб 101 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
УелЯдб 96 - ... if the rectangle contained by the whole line which cuts the circle, and the part of it without the circle be equal to the square of the line which meets it, the line which meets shall touch the circle.
УелЯдб 150 - When there are any number of magnitudes of the same kind, the first is said to have to the last of them the ratio compounded of the ratio which the first has to the second, and of the ratio whi.ch the second has to the third, and of the ratio which the third has to the fourth, and so on unto the last magnitude. For example, if A, B, C, D be four magnitudes of the same kind, the first...