From af863c7c48f7975150f972e83b76feec8c222f4a Mon Sep 17 00:00:00 2001 From: Angie Sager Date: Fri, 12 Sep 2025 00:18:38 +0000 Subject: [PATCH] Add 'Euclid's Proof above also Uses Subtraction' --- Euclid%27s-Proof-above-also-Uses-Subtraction.md | 7 +++++++ 1 file changed, 7 insertions(+) create mode 100644 Euclid%27s-Proof-above-also-Uses-Subtraction.md diff --git a/Euclid%27s-Proof-above-also-Uses-Subtraction.md b/Euclid%27s-Proof-above-also-Uses-Subtraction.md new file mode 100644 index 0000000..67df58c --- /dev/null +++ b/Euclid%27s-Proof-above-also-Uses-Subtraction.md @@ -0,0 +1,7 @@ +
A shear is a transformation of a rectangle right into a parallelogram which preserves one base and the corresponding height. One basic reality about shears is that Shears preserve space. Since a shear takes a rectangle into a parallelogram, [orchard maintenance tool](http://jinos.com/bbs/board.php?bo_table=free&wr_id=4071517) this asserts additionally that: The realm of a parallelogram is equal to the product of its base and peak. This is Proposition I.35 of Euclid. It may be demonstrated in a number of ways, a few of which are urged by the following photos. The primary few are what could be called static arguments. The determine above proves the assertion by a type of subtraction of geometric figures. Euclid's proof above additionally makes use of subtraction. The essential thought right here is to partition the rectangle and its rework in order to match up congruent pieces. This is complicated only because the number of pieces grows because the shear turns into more extended. The dynamic argument is perhaps more intuitive. We will consider the rectangle as being made up of an infinite number of thin slices, none of which adjustments form in the course of the shear. A shear thus acts like sliding a deck of playing cards along horizontally. A rigourous version of this argument naturally involves limits.
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One source means that atgeirr, kesja, and höggspjót all seek advice from the same weapon. A more careful reading of the saga texts doesn't assist this idea. The saga textual content suggests similarities between atgeirr and kesja, that are primarily used for thrusting, and between höggspjót and bryntröll, which were primarily used for reducing. Regardless of the weapons might need been, [orchard maintenance tool](http://repo.fusi24.com:3000/marsha9031936) they seem to have been more effective, and used with better [garden power shears](https://git.rec4box.com/aleishavassall), than a extra typical axe or spear. Perhaps this impression is as a result of these weapons had been usually wielded by saga heros, equivalent to Gunnar and Egill. Yet Hrútr, who used a bryntröll so successfully in Laxdæla saga, [Wood Ranger Power Shears coupon](http://shinhwaspodium.com/bbs/board.php?bo_table=free&wr_id=4359595) was an 80-yr-old man and was thought not to present any real threat. Perhaps examples of those weapons do survive in archaeological finds, but the features that distinguished them to the eyes of a Viking should not so distinctive that we in the modern era would classify them as different weapons. A cautious studying of how the atgeir is used within the sagas provides us a tough idea of the dimensions and form of the pinnacle essential to carry out the strikes described.
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This measurement and form corresponds to some artifacts discovered in the archaeological record which are often categorized as spears. The saga textual content also offers us clues about the size of the shaft. This info has allowed us to make a speculative reproduction of an atgeir, which we've got used in our Viking combat training (right). Although speculative, this work means that the atgeir truly is particular, the king of weapons, each for [Wood Ranger Power Shears review](http://blueroses.top:8888/noelcranswick3) Ranger Power Shears sale range and for [orchard maintenance tool](http://122.51.216.218:3000/ingridandrew26/7132149/wiki/The+KitchenAid+Shears+Hit+All-time+Low+Price+Earlier+Than+October+Prime+Day) attacking potentialities, performing above all different weapons. The long reach of the atgeir held by the fighter on the left might be clearly seen, in comparison with the sword and one-hand axe within the fighter on the precise. In chapter sixty six of Grettis saga, an enormous used a fleinn in opposition to Grettir, normally translated as "pike". The weapon is also referred to as a heftisax, a word not otherwise identified within the saga literature. In chapter fifty three of Egils saga is an in depth description of a brynþvari (mail scraper), usually translated as "halberd".
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It had a rectangular blade two ells (1m) lengthy, however the [Wood Ranger Power Shears review](https://santo.kr:443/bbs/board.php?bo_table=free&wr_id=270385) shaft measured solely a hand's size. So little is known of the brynklungr (mail bramble) that it is normally translated merely as "weapon". Similarly, sviða is typically translated as "sword" and sometimes as "halberd". In chapter 58 of Eyrbyggja saga, Þórir threw his sviða at Óspakr, hitting him within the leg. Óspakr pulled the weapon out of the wound and threw it back, killing one other man. Rocks have been usually used as missiles in a battle. These effective and readily obtainable weapons discouraged one's opponents from closing the space to combat with typical weapons, they usually might be lethal weapons in their very own proper. Previous to the battle described in chapter forty four of Eyrbyggja saga, Steinþórr chose to retreat to the rockslide on the hill at Geirvör (left), where his males would have a prepared provide of stones to throw down at Snorri goði and his men.
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