From 2c83aae9fe30921b309354fd698a0f05e477c9d4 Mon Sep 17 00:00:00 2001 From: Debbra Bradbury Date: Wed, 19 Nov 2025 02:25:21 +0800 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..3c9e0a2 --- /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 elementary fact about shears is that [Wood Ranger brand shears](https://kutah.top/thorstenicely3) preserve space. Since a shear takes a rectangle right into a parallelogram, this asserts also that: The world of a parallelogram is equal to the product of its base and top. That is Proposition I.35 of Euclid. It may be demonstrated in a number of methods, a few of which are recommended by the following footage. The first few are what might be referred to as static arguments. The figure above proves the assertion by a sort of subtraction of geometric figures. Euclid's proof above also uses subtraction. The fundamental thought right here is to partition the rectangle and its remodel so as to match up congruent pieces. That is complicated only because the number of items grows because the shear becomes extra extended. The dynamic argument is probably extra intuitive. We can consider the rectangle as being made up of an infinite variety of skinny slices, none of which modifications shape in the course of the shear. A shear thus acts like sliding a deck of playing cards along horizontally. A rigourous model of this argument naturally includes limits.
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One supply suggests that atgeirr, [Wood Ranger brand shears](https://library.uog.edu.et/hello-world/) kesja, and höggspjót all refer to the same weapon. A extra cautious reading of the saga texts does not help this idea. The saga text suggests similarities between atgeirr and kesja, which are primarily used for thrusting, and between höggspjót and bryntröll, which were primarily used for [buy Wood Ranger Power Shears](https://git.olyntec.com/clarissaemblin) Ranger [Power Shears](https://fs-biolink.com/petercrittende) USA cutting. Regardless of the weapons might have been, they appear to have been more effective, and used with better power, than a extra typical axe or spear. Perhaps this impression is because these weapons were usually wielded by saga heros, resembling Gunnar and Egill. Yet Hrútr, who used a bryntröll so effectively in Laxdæla saga, [Wood Ranger Power Shears specs](https://highfivedecore.com/revolutionizing-garden-care-with-wood-ranger-power-shears/) Ranger Power Shears order now was an 80-year-previous man and was thought to not present any real menace. Perhaps examples of those weapons do survive in archaeological finds, but the options that distinguished them to the eyes of a Viking aren't so distinctive that we in the trendy period would classify them as totally different weapons. A cautious reading of how the atgeir is used within the sagas gives us a rough thought of the scale and shape of the pinnacle essential to carry out the moves described.
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This measurement and form corresponds to some artifacts found within the archaeological file that are often categorized as spears. The saga text also gives us clues concerning the length of the shaft. This info has allowed us to make a speculative reproduction of an atgeir, which we've used in our Viking fight training (proper). Although speculative, this work means that the atgeir truly is particular, the king of weapons, each for range and for attacking potentialities, performing above all other weapons. The lengthy attain of the atgeir held by the fighter on the left might be clearly seen, compared to the sword and one-hand axe in the fighter on the fitting. In chapter sixty six of Grettis saga, an enormous used a fleinn against Grettir, often translated as "pike". The weapon can be referred to as a heftisax, a phrase not in any other case recognized in the saga literature. In chapter 53 of Egils saga is a detailed description of a brynþvari (mail scraper), often translated as "halberd".
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It had a rectangular blade two ells (1m) long, however the picket shaft measured only a hand's length. So little is thought of the brynklungr (mail bramble) that it is usually translated merely as "weapon". Similarly, sviða is sometimes translated as "sword" and typically as "halberd". In chapter fifty eight 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 again, killing another man. Rocks have been typically used as missiles in a fight. These effective and readily available weapons discouraged one's opponents from closing the space to struggle with conventional weapons, and so they may very well be lethal weapons in their own right. Previous to the battle described in chapter forty four of Eyrbyggja saga, Steinþórr selected to retreat to the rockslide on the hill at Geirvör (left), the place his males would have a prepared supply of stones to throw down at Snorri goði and his males.
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