 | Henry John Spooner - 1911 - 196 páginas
...Parallelogram. — The working of this problem depends upon the geometrical fact that parallelograms upon the same or equal bases, and between the same parallels, are equal in area (Euc. I. 35, 3(i). Thus, the parallelogram ABCH (Fig. 128) is on the base AB, and if on this... | |
 | St. George William Joseph Stock - 1912 - 246 páginas
...provided that we know the parallelograms to be equal. The knowledge however that parallelograms upon equal bases and between the same parallels are equal to one another does not come from intuition, but itself rests upon a prior demonstration. This (Jemonstralioji consists... | |
 | Sir Thomas Little Heath - 1921 - 610 páginas
...from Proclus's notes on Eucl. I. 36, 37 that those theorems, proving that parallelograms or triangles on the same or equal bases and between the same parallels are equal in area, appeared to the ordinary persoii paradoxical because they meant that, by moving the side opposite... | |
 | John William Gordon - 1922 - 244 páginas
...parallel lines coplanar with the lines An0, Bw0, and Cn0. Furthermore, the triangles ABD and BCE, being on equal bases and between the same parallels, are equal to one another. If to each of those triangles we add the triangle BDE we obtain the quadrilaterals ABED and BCED. Therefore... | |
 | R. H. Warn, John G. Horner - 2002 - 292 páginas
...are equal to one another. (Euc. I. 37, and I. 38.) (jr) Parallelograms upon the same base, or upon equal bases, and between the same parallels, are equal to one another. (Enc. I. 35, and I. 36.) (7i) If a parallelogram and a triangle be upon the same base, and between... | |
 | Richard Fitzpatrick - 2005 - 298 páginas
...^apaXXr]Xoiç ïaa àXXrjXoiç èaiiv OTisp sSsi ELEMENTS BOOK l Proposition 38 В С EF Triangles which are on equal bases and between the same parallels are equal to one another. Let ABC and DEF be triangles on the equal bases BC and EF, and between the same parallels BF and AD.... | |
 | 934 páginas
...same parallels, the area of triangle is equal to half the area of the parallelogram. (iv) Triangles on the same or equal bases and between the same parallels are equal in area. 3.1 Circle (i) One and only one Circle can be drawn through three non collinear points. (ii)... | |
 | Manchester univ - 1877 - 544 páginas
...your proof. State the axiom on which the proof rests, and the angles which are equal. 4. Triangles on equal bases and between the same parallels are equal to one another. If any triangle ABC, BF, and CE are taken the third parts of BA and CA and 0 is the point of intersection... | |
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Triangles upon equal bases, and between the same parallels, are equal to one another. 
